Pub Date : 2018-12-05DOI: 10.20961/JMME.V8I2.25836
Anggit Dwi Kuncoro, Ikrar Pramudya
Abstract: The concept of reflection in three-dimensional is almost the same as the concept of reflection in the two-dimensional. However, the mirror in three-dimensional is in the form of flat plane. Reflection in three-dimensional is a function that maps each point in such a way to meet the following requirements: distance between the prapeta point and the mirror is the distance between the mirror to the mapping result, the line connecting prapeta point with the mapping must be perpendicular to the mirror, and the structure and its reflection must be congruent. To get the reflection function, it can be carried out analytically. First, take flat plane as a mirror and the point that will be reflected in three-dimensional. A straight line is made through that point and it is perpendicular to the mirror, so the breakpoint can be determined. By utilizing shifts in three-dimensional, translucent point can be shifted in line with vector where is the point and is the starting point. So, the point as the result of mirroring can be obtained. The results of this study reveal that: mirroring in three-dimensional is a transformation because its function is a bijective. Reflection is involution which means that the results of twice multiplications are identity. Mirroring is not commutative. The result of twice parallel reflection composition can be called as reflection. The result of n multiplication of mirroring composition parallel to the coordinate and there is a distance is called as reflection. Keywords: Involution, Composition, Transformation.
{"title":"PENCERMINAN PADA DIMENSI TIGA","authors":"Anggit Dwi Kuncoro, Ikrar Pramudya","doi":"10.20961/JMME.V8I2.25836","DOIUrl":"https://doi.org/10.20961/JMME.V8I2.25836","url":null,"abstract":"Abstract: The concept of reflection in three-dimensional is almost the same as the concept of reflection in the two-dimensional. However, the mirror in three-dimensional is in the form of flat plane. Reflection in three-dimensional is a function that maps each point in such a way to meet the following requirements: distance between the prapeta point and the mirror is the distance between the mirror to the mapping result, the line connecting prapeta point with the mapping must be perpendicular to the mirror, and the structure and its reflection must be congruent. To get the reflection function, it can be carried out analytically. First, take flat plane as a mirror and the point that will be reflected in three-dimensional. A straight line is made through that point and it is perpendicular to the mirror, so the breakpoint can be determined. By utilizing shifts in three-dimensional, translucent point can be shifted in line with vector where is the point and is the starting point. So, the point as the result of mirroring can be obtained. The results of this study reveal that: mirroring in three-dimensional is a transformation because its function is a bijective. Reflection is involution which means that the results of twice multiplications are identity. Mirroring is not commutative. The result of twice parallel reflection composition can be called as reflection. The result of n multiplication of mirroring composition parallel to the coordinate and there is a distance is called as reflection. Keywords: Involution, Composition, Transformation.","PeriodicalId":178617,"journal":{"name":"Journal of Mathematics and Mathematics Education","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130251363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-05DOI: 10.20961/jmme.v8i1.25832
S. Rohmaniah, N. Chandra
{"title":"PENGARUH FRAILTY DALAM PEMODELAN MORTALITA","authors":"S. Rohmaniah, N. Chandra","doi":"10.20961/jmme.v8i1.25832","DOIUrl":"https://doi.org/10.20961/jmme.v8i1.25832","url":null,"abstract":"","PeriodicalId":178617,"journal":{"name":"Journal of Mathematics and Mathematics Education","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115714602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-05DOI: 10.20961/JMME.V8I2.25850
R. Marlina, B. Budiyono, Budi Usodo
Abstract : Mathematical difficulties in children with special needs (ABK) hyperactivity become a challenge for mathematics teachers in learning. The existence of curriculum targets and demands must be adjusted to the conditions of hyperactive ABK who have difficulties in terms of concentration. The purpose of this study was to describe the strategies and constraints of teachers in teaching mathematics to hyperactive ABK in inclusive class II, as well as their suitability with the conditions and needs of hyperactive ABK. This research is a qualitative field research research with purposive sampling. Samples from this study are classroom teachers who teach mathematics, Special Guidance Teachers (GPK) shadow and hyperactive ABK. The instruments used are observation, documentation and interviews. The results showed that mathematics learning for hyperactive ABK was accompanied by GPK Shadow with the approach of Individual Learning Program (PPI) in inclusive classes allowing hyperactive ABK to focus more on learning and feel comfortable because they could be with their classmates. The curriculum model used is a modified regular curriculum, including modification of goals, materials, processes and evaluations. Keywords: Mathematics Learning, Hyperactive Abk, Inclusive Class.
{"title":"ANALISIS PROSES PEMBELAJARAN MATEMATIKA ABK HIPERAKTIF DI KELAS II INKLUSIF","authors":"R. Marlina, B. Budiyono, Budi Usodo","doi":"10.20961/JMME.V8I2.25850","DOIUrl":"https://doi.org/10.20961/JMME.V8I2.25850","url":null,"abstract":"Abstract : Mathematical difficulties in children with special needs (ABK) hyperactivity become a challenge for mathematics teachers in learning. The existence of curriculum targets and demands must be adjusted to the conditions of hyperactive ABK who have difficulties in terms of concentration. The purpose of this study was to describe the strategies and constraints of teachers in teaching mathematics to hyperactive ABK in inclusive class II, as well as their suitability with the conditions and needs of hyperactive ABK. This research is a qualitative field research research with purposive sampling. Samples from this study are classroom teachers who teach mathematics, Special Guidance Teachers (GPK) shadow and hyperactive ABK. The instruments used are observation, documentation and interviews. The results showed that mathematics learning for hyperactive ABK was accompanied by GPK Shadow with the approach of Individual Learning Program (PPI) in inclusive classes allowing hyperactive ABK to focus more on learning and feel comfortable because they could be with their classmates. The curriculum model used is a modified regular curriculum, including modification of goals, materials, processes and evaluations. Keywords: Mathematics Learning, Hyperactive Abk, Inclusive Class.","PeriodicalId":178617,"journal":{"name":"Journal of Mathematics and Mathematics Education","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130407501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-05DOI: 10.20961/jmme.v8i1.25818
Nugroho Arif Sudibyo, Siti Komsatun
{"title":"PELABELAN TOTAL TAK REGULER PADA GRAF BARBEL","authors":"Nugroho Arif Sudibyo, Siti Komsatun","doi":"10.20961/jmme.v8i1.25818","DOIUrl":"https://doi.org/10.20961/jmme.v8i1.25818","url":null,"abstract":"","PeriodicalId":178617,"journal":{"name":"Journal of Mathematics and Mathematics Education","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131825403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-05DOI: 10.20961/JMME.V8I2.25846
Annisa Prima Exacta, Krisdianto Hadiprasetyo
Abstract : Differences in cognitive styles influence students’ mindset and behavior. Students with Field Independent (FI) cognitive style have different mindset with Field Dependent (FD) students. By identifying cognitive style, lecturer needs to understand the concept of material due to the way in explaining it to students. The objectives of this study are to find out: (1) students’ thinking level in Geometry who have Field Dependent (FD) cognitive style, (2) students’ thinking level in Geometry who have Field Independent (FI) cognitive style. This research is conducted at Teacher Training and Education Faculty of Veteran Bangun Nusantara Sukoharjo in Mathematics Education Department in the academic year of 2017/2018. It is a qualitative descriptive research. Data about thinking levels are obtained from diagnostic tests and interview results, while data on cognitive style are obtained from the results of Group Embedded Figure test (GEFT). Subjects are taken by purposive sampling technique and triangulation method is used as data validation. In analyzing data, the researchers employ some stages consisting of data reduction, data presentation, and conclusion. The results reveal that students’ thinking level who have Field Dependent (FD) cognitive style in Geometry course is visualization and pre-analysis, while students’ thinking level who have of Field Independent (FI) cognitive style in Geometry course is visualization, analysis, and informal pre-deduction. Keywords: Thinking Level, Cognitive Style, Field Independent (FI), Field Dependent (FD), Geometry .
{"title":"TINGKAT BERPIKIR MAHASISWA PADA MATA KULIAH GEOMETRI DITINJAU DARI GAYA KOGNITIF","authors":"Annisa Prima Exacta, Krisdianto Hadiprasetyo","doi":"10.20961/JMME.V8I2.25846","DOIUrl":"https://doi.org/10.20961/JMME.V8I2.25846","url":null,"abstract":"Abstract : Differences in cognitive styles influence students’ mindset and behavior. Students with Field Independent (FI) cognitive style have different mindset with Field Dependent (FD) students. By identifying cognitive style, lecturer needs to understand the concept of material due to the way in explaining it to students. The objectives of this study are to find out: (1) students’ thinking level in Geometry who have Field Dependent (FD) cognitive style, (2) students’ thinking level in Geometry who have Field Independent (FI) cognitive style. This research is conducted at Teacher Training and Education Faculty of Veteran Bangun Nusantara Sukoharjo in Mathematics Education Department in the academic year of 2017/2018. It is a qualitative descriptive research. Data about thinking levels are obtained from diagnostic tests and interview results, while data on cognitive style are obtained from the results of Group Embedded Figure test (GEFT). Subjects are taken by purposive sampling technique and triangulation method is used as data validation. In analyzing data, the researchers employ some stages consisting of data reduction, data presentation, and conclusion. The results reveal that students’ thinking level who have Field Dependent (FD) cognitive style in Geometry course is visualization and pre-analysis, while students’ thinking level who have of Field Independent (FI) cognitive style in Geometry course is visualization, analysis, and informal pre-deduction. Keywords: Thinking Level, Cognitive Style, Field Independent (FI), Field Dependent (FD), Geometry .","PeriodicalId":178617,"journal":{"name":"Journal of Mathematics and Mathematics Education","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133396302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-05DOI: 10.20961/jmme.v8i1.25826
Mohammad Syaiful Pradana, Awawin Mustana Rohmah
Abstract : Peat soil is an organic soil with very low carrying capacity and high compressibility. The condition is less profitable for civil engineers in building a civil foundation foundation. One method of peat soil improvement can be done with astabilization method that more environment-friendly and cheaper than other methods. Laboratory based peat stabilization studies to increase carrying capacity, reduce compression and improve peat soil physical properties have been conducted in Indonesia. The results of laboratory studies shown in the graph are still limited by time and content of the mixture. Therefore, further research is needed on the mathematical model toward the physical properties of peat soil stabilization. In this research will be formulated mathematical model of water content on the physical properties of peat soil stabilization. The model is derived from the fluid equation through porous media based on the principle of continum and controlvolume. The model is then resolved numerically by different method until MacCormack scheme with two steps are predictor step using forward difference and correctorstep using backward difference. The MacCormack scheme has the advantage of solving fluid flow equations and continuity. The model is then simulated and validated by comparing the simulation results with the real system. From the simulation results obtained the water content gradually decreased, the decrease is almost close to zero. In addition, it can be seen the difference in decrease in moisture content at each test point although in small quantities. Keywords: Moisture Content, MacCormack, Peat Soil Stabilization.
{"title":"PEMODELAN KADAR AIR PADA SIFAT FISIK STABILISASI TANAH GAMBUT","authors":"Mohammad Syaiful Pradana, Awawin Mustana Rohmah","doi":"10.20961/jmme.v8i1.25826","DOIUrl":"https://doi.org/10.20961/jmme.v8i1.25826","url":null,"abstract":"Abstract : Peat soil is an organic soil with very low carrying capacity and high compressibility. The condition is less profitable for civil engineers in building a civil foundation foundation. One method of peat soil improvement can be done with astabilization method that more environment-friendly and cheaper than other methods. Laboratory based peat stabilization studies to increase carrying capacity, reduce compression and improve peat soil physical properties have been conducted in Indonesia. The results of laboratory studies shown in the graph are still limited by time and content of the mixture. Therefore, further research is needed on the mathematical model toward the physical properties of peat soil stabilization. In this research will be formulated mathematical model of water content on the physical properties of peat soil stabilization. The model is derived from the fluid equation through porous media based on the principle of continum and controlvolume. The model is then resolved numerically by different method until MacCormack scheme with two steps are predictor step using forward difference and correctorstep using backward difference. The MacCormack scheme has the advantage of solving fluid flow equations and continuity. The model is then simulated and validated by comparing the simulation results with the real system. From the simulation results obtained the water content gradually decreased, the decrease is almost close to zero. In addition, it can be seen the difference in decrease in moisture content at each test point although in small quantities. Keywords: Moisture Content, MacCormack, Peat Soil Stabilization.","PeriodicalId":178617,"journal":{"name":"Journal of Mathematics and Mathematics Education","volume":"139 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122958739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract : Indonesia is a legal state that chooses a leader based on the results of general elections, such as the election of presidents and regional leaders. Electability is statistical data for each pair of candidates who show public interest to choose the candidate. Electability data is usually obtained from the results of questionnaires or interviews with constituents. The data search process is carried out by a survey institution. Most people discuss voluntarily in social media related to the candidate that they will choose. This study uses discussion data from social media to calculate the electability of each pair of candidates by using cluster method. The cluster method is K-Means. K-Means employs euclidean distance to determine the cluster of each data, while the number of cluster can be determined by the user. This study proposes SKM3 model (Subcontrolled K-Means Max-Min), which applies the minimum and maximum average values to decide the cluster of each data. SKM3 cluster is controlled by K-Means method that uses Euclidian distance. SKM3 model is processed using news data from detik.com site for the election of regional leader of West Java, Central Java, and East Java. The error value of SKM3 model is calculated through RMSE (Root Mean Square Error). The error value of West Java is 0.0452, the error value of Central Java up to 0.0343, and the error value of East Java is 0.2382. Based on the error values of each electoral region, it shows that SKM3 model has a small error value, so it can be concluded that SKM3 model is good for calculating the electability of the leader by using clustering method. Keywords: Electability, Clustering, K-Means, SKM3 .
{"title":"MODEL KLASTERING SKM3 (SUBCONTROLLED K-MEANS MAX-MIN) DAN APLIKASINYA DALAM MENGHITUNG ELEKTABILITAS PASANGAN CALON KEPALA DAERAH","authors":"Patuan P Tampubolon, Tesdiq Prigel Kaloka, Olivia Swasti, Widya Mustika, Alhadi Bustamam","doi":"10.20961/JMME.V8I2.25838","DOIUrl":"https://doi.org/10.20961/JMME.V8I2.25838","url":null,"abstract":"Abstract : Indonesia is a legal state that chooses a leader based on the results of general elections, such as the election of presidents and regional leaders. Electability is statistical data for each pair of candidates who show public interest to choose the candidate. Electability data is usually obtained from the results of questionnaires or interviews with constituents. The data search process is carried out by a survey institution. Most people discuss voluntarily in social media related to the candidate that they will choose. This study uses discussion data from social media to calculate the electability of each pair of candidates by using cluster method. The cluster method is K-Means. K-Means employs euclidean distance to determine the cluster of each data, while the number of cluster can be determined by the user. This study proposes SKM3 model (Subcontrolled K-Means Max-Min), which applies the minimum and maximum average values to decide the cluster of each data. SKM3 cluster is controlled by K-Means method that uses Euclidian distance. SKM3 model is processed using news data from detik.com site for the election of regional leader of West Java, Central Java, and East Java. The error value of SKM3 model is calculated through RMSE (Root Mean Square Error). The error value of West Java is 0.0452, the error value of Central Java up to 0.0343, and the error value of East Java is 0.2382. Based on the error values of each electoral region, it shows that SKM3 model has a small error value, so it can be concluded that SKM3 model is good for calculating the electability of the leader by using clustering method. Keywords: Electability, Clustering, K-Means, SKM3 .","PeriodicalId":178617,"journal":{"name":"Journal of Mathematics and Mathematics Education","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126541606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-05DOI: 10.20961/JMME.V8I2.25852
Fatriya Adamura, Vera Dewi Susanti
Abstract : Mathematical reasoning ability is needed by students both in the process of understanding mathematics and in everyday life context. In fact, Indonesian students’ ability in the field of mathematics is still very low. Referring to the fact, this study is attempted to determine students' mathematical reasoning in solving real analysis problems based on their ability to think intuitively. This study is a qualitative descriptive research. The data sources in this study are college students. Data are collected through written tests and interview. Data analysis in this study is carried out by stages of data reduction, data presentation, and conclusion. The results show that (1) Students with high intuitive thinking skills in real analysis problem solving have a tendency to implement mathematical reasoning perfectly. They are able to carry out mathematical reasoning at each stage of solving real analysis problems. (2) Students with medium intuitive thinking ability in solving real analysis problem have a tendency to implement mathematical reasoning less perfectly. They are not able to carry out mathematical reasoning at the stage of solving problems according to plan and re-checking it again. (3) Students with low intuitive thinking skill in solving real analysis problem have a tendency to implement mathematical reasoning imperfectly. They are unable to carry out mathematical reasoning at the stage of planning solution and solving problem. Keywords: mathematical reasoning, solving problem, intuitive .
{"title":"PENALARAN MATEMATIS MAHASISWA DALAM MEMECAHKAN MASALAH ANALISIS REAL BERDASARKAN KEMAMPUAN BERPIKIR INTUITIF","authors":"Fatriya Adamura, Vera Dewi Susanti","doi":"10.20961/JMME.V8I2.25852","DOIUrl":"https://doi.org/10.20961/JMME.V8I2.25852","url":null,"abstract":"Abstract : Mathematical reasoning ability is needed by students both in the process of understanding mathematics and in everyday life context. In fact, Indonesian students’ ability in the field of mathematics is still very low. Referring to the fact, this study is attempted to determine students' mathematical reasoning in solving real analysis problems based on their ability to think intuitively. This study is a qualitative descriptive research. The data sources in this study are college students. Data are collected through written tests and interview. Data analysis in this study is carried out by stages of data reduction, data presentation, and conclusion. The results show that (1) Students with high intuitive thinking skills in real analysis problem solving have a tendency to implement mathematical reasoning perfectly. They are able to carry out mathematical reasoning at each stage of solving real analysis problems. (2) Students with medium intuitive thinking ability in solving real analysis problem have a tendency to implement mathematical reasoning less perfectly. They are not able to carry out mathematical reasoning at the stage of solving problems according to plan and re-checking it again. (3) Students with low intuitive thinking skill in solving real analysis problem have a tendency to implement mathematical reasoning imperfectly. They are unable to carry out mathematical reasoning at the stage of planning solution and solving problem. Keywords: mathematical reasoning, solving problem, intuitive .","PeriodicalId":178617,"journal":{"name":"Journal of Mathematics and Mathematics Education","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127840819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-05DOI: 10.20961/JMME.V8I1.25820
P. R. Musthofa, Yemi Kuswardi
Abstract:Graph theory is a branch of mathematics that facilitates problem solving. There are a lot of researches which concern on this issue. Various kinds of terms are introduced, one of them is graph decomposition. Graph decomposition is sub graphs collection of non-empty G graph {Hi} until Hi = 〈Ei〉 for non-empty sub graph Ei of E (G), where {Ei} is a partition of E (G). Sub graph Hi in decomposition G do not contain of isolated points. If {Hi} is a decomposition of G, it is denoted by .The discussion of graph decomposition can be developed in graph decomposition through various types. One of the types is decomposition of sun graphs. Sun graph is a graph formed from a circle Cn in which each vertex on a circle graph is given one additional vertex with a degree. So, each vertex in sun graph has 3 degrees, except the edge of cortex which only have 1 degree. The sun graph is the result of corona between two graphs, namely a circular graph with n vertex and complement of a complete graph with 1 number of vertex . The sun graph is denoted by where n is the number of vertex in circle graph. If the vertex naming refers to one vertex (with clockwise rules) and additional vertex naming connected to a circle vertex graph (vi), where the additional vertex has a degree of one, then the rule of naming is and sun graph is partitioned into a sub graph H_i = 〈Ei〉 in the form of K 2 where i ≠ j so that H_i∩H_j = ∅, for i = 1,2,3, ..., n with sub graph If every i + 1, i + 2> n has an implicit + 1 and i + 2 will be expressed as an integers 1,2,3, ..., n (mod n), then the sun graph is 2K 2- decomposition. So, for sun graph n ≥3 is 2K2-decomposition. Keywords: Decomposition, Sun Graph .
摘要:图论是数学的一个分支，它有助于解决问题。有很多研究都在关注这个问题。引入了各种各样的术语，其中之一就是图分解。图分解是E (G)的非空子图Ei在Hi = < Ei >之前的非空G图{Hi}的子图集合，其中{Ei}是E (G)的一个分区。分解G中的子图Hi不包含孤立点。如果{Hi}是G的分解，则表示为。图分解的讨论可以通过各种类型在图分解中展开。其中一种是太阳图的分解。太阳图是由圆Cn构成的图，其中圆图上的每个顶点都有一个附加的顶点，顶点的度数为1。所以，太阳图中的每个顶点都有3度，除了皮质的边缘只有1度。太阳图是两个图之间的电晕的结果，即一个有n个顶点的圆图和一个有1个顶点的完全图的补。太阳图表示为，其中n为圆图中的顶点数。如果顶点命名是指一个顶点(按顺时针规则)和附加顶点命名连接到一个圆顶点图(vi)上，其中附加顶点的度数为1，则命名规则为，太阳图划分为K 2形式的子图H_i = < Ei >，其中i≠j，使得H_i∩H_j =∅，对于i = 1,2,3，…如果每一个i + 1, i + 2> n都有一个隐式的+ 1，并且i + 2将被表示为整数1,2,3，…， n (mod n)，则太阳图为2K -分解。因此，对于太阳图n≥3为2k2分解。关键词:分解;太阳图;
{"title":"DEKOMPOSISI GRAF MATAHARI","authors":"P. R. Musthofa, Yemi Kuswardi","doi":"10.20961/JMME.V8I1.25820","DOIUrl":"https://doi.org/10.20961/JMME.V8I1.25820","url":null,"abstract":"Abstract:Graph theory is a branch of mathematics that facilitates problem solving. There are a lot of researches which concern on this issue. Various kinds of terms are introduced, one of them is graph decomposition. Graph decomposition is sub graphs collection of non-empty G graph {Hi} until Hi = 〈Ei〉 for non-empty sub graph Ei of E (G), where {Ei} is a partition of E (G). Sub graph Hi in decomposition G do not contain of isolated points. If {Hi} is a decomposition of G, it is denoted by .The discussion of graph decomposition can be developed in graph decomposition through various types. One of the types is decomposition of sun graphs. Sun graph is a graph formed from a circle Cn in which each vertex on a circle graph is given one additional vertex with a degree. So, each vertex in sun graph has 3 degrees, except the edge of cortex which only have 1 degree. The sun graph is the result of corona between two graphs, namely a circular graph with n vertex and complement of a complete graph with 1 number of vertex . The sun graph is denoted by where n is the number of vertex in circle graph. If the vertex naming refers to one vertex (with clockwise rules) and additional vertex naming connected to a circle vertex graph (vi), where the additional vertex has a degree of one, then the rule of naming is and sun graph is partitioned into a sub graph H_i = 〈Ei〉 in the form of K 2 where i ≠ j so that H_i∩H_j = ∅, for i = 1,2,3, ..., n with sub graph If every i + 1, i + 2> n has an implicit + 1 and i + 2 will be expressed as an integers 1,2,3, ..., n (mod n), then the sun graph is 2K 2- decomposition. So, for sun graph n ≥3 is 2K2-decomposition. Keywords: Decomposition, Sun Graph .","PeriodicalId":178617,"journal":{"name":"Journal of Mathematics and Mathematics Education","volume":"319 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125742731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-05DOI: 10.20961/jmme.v8i1.25816
Silfiatul Khoiriah, Tri Atmojo Kusmayadi
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