Pub Date : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4912
Javier Hassan, Jahiri Manditong, Alcyn Bakkang, Sisteta U. Kamdon, Jeffrey Imer Salim
Let G be a graph with no isolated vertex. A subset M ⊆ V (G) is called a J-open set if NG(a)NG(b) ̸= ∅ and NG(b)NG(a) ̸= ∅ ∀ a, b ∈ M, where a ̸= b. If in addition, M is a total dominating in G, then we call M a J-total dominating set in G. The maximum cardinality amongall J-total dominating set in G, denoted by γJt(G), is called the J-total domination number of G. In this paper, we characterize J-total dominating sets in some special graphs and join of two graphs, and we use these results to obtain formulas for the parameters of these graphs. Moreover, we determine its relationships with other known parameters in graph theory. Finally, we derive the lower bound of the parameter for the corona of two graphs.
{"title":"Characterizations of $J$-Total Dominating Sets in Some Special Graphs and Graphs under Some Operations","authors":"Javier Hassan, Jahiri Manditong, Alcyn Bakkang, Sisteta U. Kamdon, Jeffrey Imer Salim","doi":"10.29020/nybg.ejpam.v16i4.4912","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4912","url":null,"abstract":"Let G be a graph with no isolated vertex. A subset M ⊆ V (G) is called a J-open set if NG(a)NG(b) ̸= ∅ and NG(b)NG(a) ̸= ∅ ∀ a, b ∈ M, where a ̸= b. If in addition, M is a total dominating in G, then we call M a J-total dominating set in G. The maximum cardinality amongall J-total dominating set in G, denoted by γJt(G), is called the J-total domination number of G. In this paper, we characterize J-total dominating sets in some special graphs and join of two graphs, and we use these results to obtain formulas for the parameters of these graphs. Moreover, we determine its relationships with other known parameters in graph theory. Finally, we derive the lower bound of the parameter for the corona of two graphs.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"36 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069136","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4914
Sergio Canoy Jr, Ferdinand Jamil, Sheila Menchavez
Given a simple graph $G=(V(G),E(G))$, a function $f:V(G)to {0,1,2}$ is a hop Italian dominating function if for every vertex $v$ with $f(v)=0$ there exists a vertex $u$ with $f(u)=2$ for which $u$ and $v$ are of distance $2$ from each other or there exist two vertices $w$ and $z$ for which $f(w)=1=f(z)$ and each of $w$ and $z$ is of distance $2$ from $v$. The minimum weight $sum_{vin V(G)}f(v)$ of a hop Italian dominating function is the hop Italian domination number of $G$, and is denoted by $gamma_{hI}(G)$. In this paper, we initiate the study of the hop Italian domination. In particular, we establish some properties of the the hop Italian dominating function and explore the relationships of the hop Italian domination number with the hop Roman domination number cite{Rad2,Natarajan} and with the $2$-hop domination number cite{Canoy}. We study the concept under some binary graph operations. We establish tight bounds and determine exact values for their respective hop Italian domination numbers.
{"title":"Hop Italian Domination in Graphs","authors":"Sergio Canoy Jr, Ferdinand Jamil, Sheila Menchavez","doi":"10.29020/nybg.ejpam.v16i4.4914","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4914","url":null,"abstract":"Given a simple graph $G=(V(G),E(G))$, a function $f:V(G)to {0,1,2}$ is a hop Italian dominating function if for every vertex $v$ with $f(v)=0$ there exists a vertex $u$ with $f(u)=2$ for which $u$ and $v$ are of distance $2$ from each other or there exist two vertices $w$ and $z$ for which $f(w)=1=f(z)$ and each of $w$ and $z$ is of distance $2$ from $v$. The minimum weight $sum_{vin V(G)}f(v)$ of a hop Italian dominating function is the hop Italian domination number of $G$, and is denoted by $gamma_{hI}(G)$. In this paper, we initiate the study of the hop Italian domination. In particular, we establish some properties of the the hop Italian dominating function and explore the relationships of the hop Italian domination number with the hop Roman domination number cite{Rad2,Natarajan} and with the $2$-hop domination number cite{Canoy}. We study the concept under some binary graph operations. We establish tight bounds and determine exact values for their respective hop Italian domination numbers.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069138","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4924
Hamed Ouédraogo, Abdoulaye Dembega, André Conseibo
In this paper we study a class of commutative non associative algebras satisfying a polynomial identity of degree five. We show that under the assumption of the existence of a non-zero idempotent, any commutative algebra verifying such an identity admits a Peirce decomposition. Using this decomposition we proceeded to the study of the derivations and representations of algebras of this class.
{"title":"Derivations and Representations of Commutative Algebras Verifying a Polynomial Identity of Degree Five","authors":"Hamed Ouédraogo, Abdoulaye Dembega, André Conseibo","doi":"10.29020/nybg.ejpam.v16i4.4924","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4924","url":null,"abstract":"In this paper we study a class of commutative non associative algebras satisfying a polynomial identity of degree five. We show that under the assumption of the existence of a non-zero idempotent, any commutative algebra verifying such an identity admits a Peirce decomposition. Using this decomposition we proceeded to the study of the derivations and representations of algebras of this class.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"204 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069307","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}
In this paper, we introduce one interesting mathematical tool namely, (s, v)*-dense, and analyze its nature in a bigeneralized topological space. Further, we prove some properties of this set and give the relationship between (s, v)-dense and (s, v)*-dense sets. Finally, we give some applications for various sets defined in a bigeneralized topological space.
{"title":"On Dense Sets","authors":"None Diaa Elgezouli, None Mutaz Omer, Yasser Farhat, None Elmhadi Afif, Vadakasi Subramanian","doi":"10.29020/nybg.ejpam.v16i4.4944","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4944","url":null,"abstract":"In this paper, we introduce one interesting mathematical tool namely, (s, v)*-dense, and analyze its nature in a bigeneralized topological space. Further, we prove some properties of this set and give the relationship between (s, v)-dense and (s, v)*-dense sets. Finally, we give some applications for various sets defined in a bigeneralized topological space.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"73 12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068825","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4883
Javier Hassan, Jeffrey Imer Salim
Let G be a graph. A subset D = {d1, d2, · · · , dm} of vertices of G is called a J-set ifNG[di] NG[dj ] ̸= ∅ for every i ̸= j, where i, j ∈ {1, 2, . . . , m}. A J-set is called a J-dominatingset of G if D = {d1, d2, . . . , dm} is a dominating set of G. The J-domination number of G, denotedby γJ (G), is the maximum cardinality of a J-dominating set of G. In this paper, we introducethis new concept and we establish formulas and properties on some classes of graphs and in joinof two graphs. Upper and lower bounds of J-domination parameter with respect to the order of agraph and other parameters in graph theory are obtained. In addition, we present realization resultinvolving this parameter and the standard domination. Moreover, we characterize J-dominatingsets in some classes of graphs and join of two graphs and finally determine the exact value of theparameter of each of these graphs.
{"title":"J-Domination in Graphs","authors":"Javier Hassan, Jeffrey Imer Salim","doi":"10.29020/nybg.ejpam.v16i4.4883","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4883","url":null,"abstract":"Let G be a graph. A subset D = {d1, d2, · · · , dm} of vertices of G is called a J-set ifNG[di] NG[dj ] ̸= ∅ for every i ̸= j, where i, j ∈ {1, 2, . . . , m}. A J-set is called a J-dominatingset of G if D = {d1, d2, . . . , dm} is a dominating set of G. The J-domination number of G, denotedby γJ (G), is the maximum cardinality of a J-dominating set of G. In this paper, we introducethis new concept and we establish formulas and properties on some classes of graphs and in joinof two graphs. Upper and lower bounds of J-domination parameter with respect to the order of agraph and other parameters in graph theory are obtained. In addition, we present realization resultinvolving this parameter and the standard domination. Moreover, we characterize J-dominatingsets in some classes of graphs and join of two graphs and finally determine the exact value of theparameter of each of these graphs.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"25 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068992","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4972
Ahlam Ahmed Alharbi, Adem Kilicman
The principle objective of this research is to present generalised functions ideas which are: fuzzy generalised continuous, generalized strongly continuous, generalized irresolute, generalized open and closed mapping, and the last part is the homomorphism in fuzzy bitopological spaces. We also study the relationships between them, their characteristics, their composition, and some important theories and counterexamples.
{"title":"Generalized Different Types of Mappings in Fuzzy Bitopological Spaces","authors":"Ahlam Ahmed Alharbi, Adem Kilicman","doi":"10.29020/nybg.ejpam.v16i4.4972","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4972","url":null,"abstract":"The principle objective of this research is to present generalised functions ideas which are: fuzzy generalised continuous, generalized strongly continuous, generalized irresolute, generalized open and closed mapping, and the last part is the homomorphism in fuzzy bitopological spaces. We also study the relationships between them, their characteristics, their composition, and some important theories and counterexamples.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"87 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069703","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4829
Ayesha Alorini, Aymen Ben Amira, Mohammad Alzohairi, Moncef Bouaziz
A graph G consists of a finite set V (G) of vertices with a collection E(G) of unordered pairs of distinct vertices called edge set of G. Let G be a graph. A set M of vertices is a module of G if, for vertices x and y in M and each vertex z outside M, {z, x} ∈ E(G) ⇐⇒ {z, y} ∈ E(G). Thus, a module of G is a set M of vertices indistinguishable by the vertices outside M. The empty set, the singleton sets and the full set of vertices represent the trivial modules. A graph is indecomposable if all its modules are trivial, otherwise it is decomposable. Indecomposable graphs with at least four vertices are prime graphs. The introduction and the study of the construction of prime graphs obtained from a given decomposable graph by adding one edge constitue the central points of this paper.
{"title":"Prime Graph Generation through Single Edge Addition: Characterizing a Class of Graphs","authors":"Ayesha Alorini, Aymen Ben Amira, Mohammad Alzohairi, Moncef Bouaziz","doi":"10.29020/nybg.ejpam.v16i4.4829","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4829","url":null,"abstract":"A graph G consists of a finite set V (G) of vertices with a collection E(G) of unordered pairs of distinct vertices called edge set of G. Let G be a graph. A set M of vertices is a module of G if, for vertices x and y in M and each vertex z outside M, {z, x} ∈ E(G) ⇐⇒ {z, y} ∈ E(G). Thus, a module of G is a set M of vertices indistinguishable by the vertices outside M. The empty set, the singleton sets and the full set of vertices represent the trivial modules. A graph is indecomposable if all its modules are trivial, otherwise it is decomposable. Indecomposable graphs with at least four vertices are prime graphs. The introduction and the study of the construction of prime graphs obtained from a given decomposable graph by adding one edge constitue the central points of this paper.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"128 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136107072","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}
This article presents a mathematical model of the COVID-19 transmission mechanism, considering therapeutic interventions like immunization and recovery or treatment. The model shows that the disease-free and endemic equilibriums are globally asymptotically stable when effective reproduction numbers are less than or larger than unity. The critical vaccination thresholddepends on the vaccine’s ability to prevent or cure the illness. The model predicts the effectiveness of vaccination based on factors like vaccination efficiency, scheduling, and relaxation of social measures. The subsiding of the epidemic as vaccination is implemented depends on the scale of relaxation of social measures.
{"title":"A simulation Model of COVID-19 Epidemic Based on Vaccination and Treatment","authors":"Fahdah Alshammari, Alaa Mustafa, Ehssan Omer, Fatima Omer","doi":"10.29020/nybg.ejpam.v16i4.4805","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4805","url":null,"abstract":"This article presents a mathematical model of the COVID-19 transmission mechanism, considering therapeutic interventions like immunization and recovery or treatment. The model shows that the disease-free and endemic equilibriums are globally asymptotically stable when effective reproduction numbers are less than or larger than unity. The critical vaccination thresholddepends on the vaccine’s ability to prevent or cure the illness. The model predicts the effectiveness of vaccination based on factors like vaccination efficiency, scheduling, and relaxation of social measures. The subsiding of the epidemic as vaccination is implemented depends on the scale of relaxation of social measures.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"38 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069134","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 : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4870
Jhon Cris Bonifacio, Clarence Joy Andaya, Daryl Magpantay
This paper defines a new class of graphs using the spanning subgraphs of a cycle graph as vertices. This class of graphs is called $j$-edge intersection graph of cycle graph, denoted by $E_{C_{(n,j)}}$. The vertex set of $E_{C_{(n,j)}}$ is the set of spanning subgraphs of cycle graph with $j$ edges where $n geq 3$ and $j$ is a nonnegative integer such that $1 leq j leq n$. Moreover, two distinct vertices are adjacent if they have exactly one edge in common. $E_{C_{(n,j)}}$ is considered as a simple graph. Furthermore, $E_{C_{(n,j)}}$ is characterized by the value of $j$ that is when $j=1$ or $lceil frac{n}{2} rceil < j leq n$ and $2 leq j leq lceil frac{n}{2} rceil$. When $j=1$ or $lceil frac{n}{2} rceil < j leq n$, the new graph only produced an empty graph. Hence, the proponents only considered the value when $2 leq j leq lceil frac{n}{2} rceil$ in determining the order and size of $E_{C_{(n,j)}}$. Moreover, this paper discusses necessary and sufficient conditions where the $j$-edge intersection graph of $C_n$ is isomorphic to the cycle graph. Furthermore, the researchers determined a lower bound for the independence number, and an upper bound for the domination number of $E_{C_{(n,j)}}$ when $j=2$.
{"title":"On the j-Edge Intersection Graph of Cycle Graph","authors":"Jhon Cris Bonifacio, Clarence Joy Andaya, Daryl Magpantay","doi":"10.29020/nybg.ejpam.v16i4.4870","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4870","url":null,"abstract":"This paper defines a new class of graphs using the spanning subgraphs of a cycle graph as vertices. This class of graphs is called $j$-edge intersection graph of cycle graph, denoted by $E_{C_{(n,j)}}$. The vertex set of $E_{C_{(n,j)}}$ is the set of spanning subgraphs of cycle graph with $j$ edges where $n geq 3$ and $j$ is a nonnegative integer such that $1 leq j leq n$. Moreover, two distinct vertices are adjacent if they have exactly one edge in common. $E_{C_{(n,j)}}$ is considered as a simple graph. Furthermore, $E_{C_{(n,j)}}$ is characterized by the value of $j$ that is when $j=1$ or $lceil frac{n}{2} rceil < j leq n$ and $2 leq j leq lceil frac{n}{2} rceil$. When $j=1$ or $lceil frac{n}{2} rceil < j leq n$, the new graph only produced an empty graph. Hence, the proponents only considered the value when $2 leq j leq lceil frac{n}{2} rceil$ in determining the order and size of $E_{C_{(n,j)}}$. Moreover, this paper discusses necessary and sufficient conditions where the $j$-edge intersection graph of $C_n$ is isomorphic to the cycle graph. Furthermore, the researchers determined a lower bound for the independence number, and an upper bound for the domination number of $E_{C_{(n,j)}}$ when $j=2$.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069148","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4733
C. Boonpok, M. Thongmoon
This paper deals with the notion of $delta p(Lambda,p)$-open sets. Some properties of $delta p(Lambda,p)$-open sets and $delta p(Lambda,p)$-closed sets are investigated. Moreover, several characterizations of $delta p(Lambda,p)$-$mathscr{D}_1$ spaces and $delta p(Lambda,p)$-$R_0$ spaces are established.
{"title":"$delta p(Lambda,p)$-open Sets in Topological Spaces","authors":"C. Boonpok, M. Thongmoon","doi":"10.29020/nybg.ejpam.v16i3.4733","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4733","url":null,"abstract":"This paper deals with the notion of $delta p(Lambda,p)$-open sets. Some properties of $delta p(Lambda,p)$-open sets and $delta p(Lambda,p)$-closed sets are investigated. Moreover, several characterizations of $delta p(Lambda,p)$-$mathscr{D}_1$ spaces and $delta p(Lambda,p)$-$R_0$ spaces are established.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42817370","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}
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