Pub Date : 2022-08-17DOI: 10.1080/09720529.2021.2015090
Ting Zhou, Zhen Lin, L. Miao
{"title":"The extremal Sombor index of trees and unicyclic graphs with given matching number","authors":"Ting Zhou, Zhen Lin, L. Miao","doi":"10.1080/09720529.2021.2015090","DOIUrl":"https://doi.org/10.1080/09720529.2021.2015090","url":null,"abstract":"","PeriodicalId":46563,"journal":{"name":"JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43632016","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 : 2022-07-04DOI: 10.1080/09720529.2022.2083152
H. Shlaka, F. Kareem
Abstract Let A associative algebra (finite dimensional over ) of any characteristic with involution * and let K = skew(A) = {a ∈ A|a* = -a} be its corresponding sub-algebra under the Lie product [a, b] = ab - ba for all a, b ∈ A. If A = End V for some finite dimensional vector space over and * is an adjoint involution with a symmetric non-alternating bilinear form on V, then * is said to be orthogonal. In this paper, abelian inner ideals which are non Jordan-Lie of such Lie algebras were defined, considered, studied, and classified. Some examples and results were provided. It is proved that every abelian inner ideal which is non Jordan-Lie B of K can be expressed as B = {v, H ⊥}, where v is an isotropic vector of a hyperbolic plane H ⊆ V and H ⊥ is the orthogonal subspace of H.
{"title":"Abelian Non Jordan-Lie Inner Ideals of the Orthogonal Finite Dimensional Lie Algebras","authors":"H. Shlaka, F. Kareem","doi":"10.1080/09720529.2022.2083152","DOIUrl":"https://doi.org/10.1080/09720529.2022.2083152","url":null,"abstract":"Abstract Let A associative algebra (finite dimensional over ) of any characteristic with involution * and let K = skew(A) = {a ∈ A|a* = -a} be its corresponding sub-algebra under the Lie product [a, b] = ab - ba for all a, b ∈ A. If A = End V for some finite dimensional vector space over and * is an adjoint involution with a symmetric non-alternating bilinear form on V, then * is said to be orthogonal. In this paper, abelian inner ideals which are non Jordan-Lie of such Lie algebras were defined, considered, studied, and classified. Some examples and results were provided. It is proved that every abelian inner ideal which is non Jordan-Lie B of K can be expressed as B = {v, H ⊥}, where v is an isotropic vector of a hyperbolic plane H ⊆ V and H ⊥ is the orthogonal subspace of H.","PeriodicalId":46563,"journal":{"name":"JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY","volume":"25 1","pages":"1547 - 1561"},"PeriodicalIF":1.4,"publicationDate":"2022-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42837685","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 : 2022-07-04DOI: 10.1080/09720529.2022.2063543
I. H. Agustin, L. Susilowati, Dafik, I. N. Cangul, N. Mohanapriya
Abstract A total k-labeling is defined as a function g from the edge set to the first natural number ke and a function f from the vertex set to a non-negative even number up to 2kv , where k = max{ke , 2kv }. A vertex irregular reflexive k-labeling of the graph G is total k-labeling if wt(x) ¹ wt(x¢) for every two different vertices x and x¢ of G, where wt(x) = f (x) + Σ xy ∈E(G) g(xy). The reflexive vertex strength of the graph G, denoted by rvs(G), is the minimum k for a graph G with a vertex irregular reflexive k-labeling. We will determine the exact value of rvs(G) in this paper, where G is a regular and regular-like graph. A regular graph is a graph where each vertex has the same number of neighbors. A regular graph with all vertices of degree r is called an r-regular graph or regular graph of degree r. A regular-like graphs is an almost regular graph that we develop in a new definition and we called it with (s, r) -almost regular graphs.
摘要将全k标记定义为从边集到第一个自然数ke的函数g和从顶点集到最大2kv的非负偶数的函数f，其中k = max{ke, 2kv}。图G的顶点不规则自反k标记是总k标记，如果对于G的每两个不同的顶点x和x¢，wt(x)¹wt(x¢)，其中wt(x) = f (x) + Σ xy∈E(G) G (xy)。图G的自反顶点强度，用rvs(G)表示，是具有顶点不规则自反k标记的图G的最小k。我们将在本文中确定rvs(G)的确切值，其中G是一个正则和类正则图。正则图是指每个顶点都有相同数量的邻居的图。所有顶点为r度的正则图称为r-正则图或r度的正则图。类正则图是我们在新定义中发展的一种几乎正则图，我们称之为(s, r) -几乎正则图。
{"title":"On the vertex irregular reflexive labeling of several regular and regular-like graphs","authors":"I. H. Agustin, L. Susilowati, Dafik, I. N. Cangul, N. Mohanapriya","doi":"10.1080/09720529.2022.2063543","DOIUrl":"https://doi.org/10.1080/09720529.2022.2063543","url":null,"abstract":"Abstract A total k-labeling is defined as a function g from the edge set to the first natural number ke and a function f from the vertex set to a non-negative even number up to 2kv , where k = max{ke , 2kv }. A vertex irregular reflexive k-labeling of the graph G is total k-labeling if wt(x) ¹ wt(x¢) for every two different vertices x and x¢ of G, where wt(x) = f (x) + Σ xy ∈E(G) g(xy). The reflexive vertex strength of the graph G, denoted by rvs(G), is the minimum k for a graph G with a vertex irregular reflexive k-labeling. We will determine the exact value of rvs(G) in this paper, where G is a regular and regular-like graph. A regular graph is a graph where each vertex has the same number of neighbors. A regular graph with all vertices of degree r is called an r-regular graph or regular graph of degree r. A regular-like graphs is an almost regular graph that we develop in a new definition and we called it with (s, r) -almost regular graphs.","PeriodicalId":46563,"journal":{"name":"JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY","volume":"25 1","pages":"1457 - 1473"},"PeriodicalIF":1.4,"publicationDate":"2022-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47613200","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 : 2022-07-04DOI: 10.1080/09720529.2022.2026625
Sharmin Sultana, H. Akter, P. Dey
Abstract We were able to classify all 1-error correcting [5, 3] codes over GF(5) in paper [1] and [5, 2] ternary codes in paper [2]. Now, our focus is an equivalence based classification of error correcting linear codes of length 6 over GF(5). In paper [3], we investigated the equivalence of [6,3,4] codes of length 6 and dimension 3 over GF(4). In this paper we classify the [6,3,4] codes over GF(5). We explore the weight distribution of these codes as well as their duals.
{"title":"An equivalence based classification of [6, 3, 4] error correcting codes over GF(5)","authors":"Sharmin Sultana, H. Akter, P. Dey","doi":"10.1080/09720529.2022.2026625","DOIUrl":"https://doi.org/10.1080/09720529.2022.2026625","url":null,"abstract":"Abstract We were able to classify all 1-error correcting [5, 3] codes over GF(5) in paper [1] and [5, 2] ternary codes in paper [2]. Now, our focus is an equivalence based classification of error correcting linear codes of length 6 over GF(5). In paper [3], we investigated the equivalence of [6,3,4] codes of length 6 and dimension 3 over GF(4). In this paper we classify the [6,3,4] codes over GF(5). We explore the weight distribution of these codes as well as their duals.","PeriodicalId":46563,"journal":{"name":"JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY","volume":"25 1","pages":"1425 - 1434"},"PeriodicalIF":1.4,"publicationDate":"2022-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42708786","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 : 2022-07-04DOI: 10.1080/09720529.2022.2060608
Uraiwan Jittburus, P. Julatha, Aiyared Iampan
Abstract The main aims of this paper are to introduce the concept of an INF-hesitant fuzzy ideal in a semigroup and its INF-hesitant fuzzy translations, and to investigate their properties. Further, characterizations of the INF-hesitant fuzzy ideal are given in terms of sets, fuzzy sets, Pythagorean fuzzy sets, interval-valued fuzzy sets, hesitant fuzzy sets, and its INF-hesitant fuzzy translations.
{"title":"INF-hesitant fuzzy ideals of semigroups and their INF-hesitant fuzzy translations","authors":"Uraiwan Jittburus, P. Julatha, Aiyared Iampan","doi":"10.1080/09720529.2022.2060608","DOIUrl":"https://doi.org/10.1080/09720529.2022.2060608","url":null,"abstract":"Abstract The main aims of this paper are to introduce the concept of an INF-hesitant fuzzy ideal in a semigroup and its INF-hesitant fuzzy translations, and to investigate their properties. Further, characterizations of the INF-hesitant fuzzy ideal are given in terms of sets, fuzzy sets, Pythagorean fuzzy sets, interval-valued fuzzy sets, hesitant fuzzy sets, and its INF-hesitant fuzzy translations.","PeriodicalId":46563,"journal":{"name":"JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY","volume":"25 1","pages":"1487 - 1507"},"PeriodicalIF":1.4,"publicationDate":"2022-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47662577","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 : 2022-07-04DOI: 10.1080/09720529.2022.2082724
Eman Ayed Naim, Akeel Ramadan Mehdi
Abstract As a proper generalization of pseudo-injectivity, we introduce and investigate gs-pseudo-injective modules. A right module M over a ring R is said to be gs-pseudo- N -injective (where N is a right R -module) if every R -monomorphism from a submodule of soc ( N ) soc ( RR ) into M extends to N. A module M is said to be gs-pseudo-injective, if M is gs-pseudo-M-injective. We obtain various characterizations and properties of these modules. Some results on pseudo-injectivity are extended to gs-pseudo-injectivity.
摘要作为伪注入性的适当推广，我们引入并研究了gs-伪注入模。如果从soc (N) soc (RR)的子模到M的每一个R -单态扩展到N，则称环R上的右模M是gs-伪- N -内射(其中N是一个右R -模)，如果M是gs-伪-M-内射，则称模M是gs-伪- N -内射。我们得到了这些模块的各种表征和性质。将拟注入性的一些结果推广到gs-拟注入性。
{"title":"On gs-pseudo-injective modules","authors":"Eman Ayed Naim, Akeel Ramadan Mehdi","doi":"10.1080/09720529.2022.2082724","DOIUrl":"https://doi.org/10.1080/09720529.2022.2082724","url":null,"abstract":"Abstract As a proper generalization of pseudo-injectivity, we introduce and investigate gs-pseudo-injective modules. A right module M over a ring R is said to be gs-pseudo- N -injective (where N is a right R -module) if every R -monomorphism from a submodule of soc ( N ) soc ( RR ) into M extends to N. A module M is said to be gs-pseudo-injective, if M is gs-pseudo-M-injective. We obtain various characterizations and properties of these modules. Some results on pseudo-injectivity are extended to gs-pseudo-injectivity.","PeriodicalId":46563,"journal":{"name":"JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY","volume":"25 1","pages":"1535 - 1545"},"PeriodicalIF":1.4,"publicationDate":"2022-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45732267","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 : 2022-06-20DOI: 10.1080/09720529.2022.2067390
Tayyiba Sattar, M. S. Sardar, M. Alaeiyan, M. R. Farahani, M. Cancan, Ziyattin Taş
Abstract In graph coloring, labels are assigned to graph elements according to certain constraints. Colors are a special case of graph labeling as well as in practical applications, graph coloring also poses some theoretical challenges. A topic related to graph coloring will be discussed in this study, i.e., b-chromatic number. In proper coloring, edges, vertices, or both of them are colored so that they are distinct from one another. A b-coloring of m colors of a graph G is similar to proper coloring in which at least one vertex from each color class is connected to (m-1) other colors. The b-chromatic number of a graph G is the greatest positive number k such that G admits a b-coloring with k colors and is represented by ϕ(G). Fractals are geometric objects that are self-similar at multiple scales and their geometric measurements are different from fractal measurements. In this paper, we will evaluate the b-chromatic number of Fractal type graphs, i.e., Sierpinski network S(n; Kk) (where Kk is a complete graph of order k) and Sierpinski gasket network S(n). Firstly, we will compute the b-chromatic number of S(n; K3), S(n; K4) and S(n; K5) for n ≥ 2. After that, we will generalize the result for the Sierpinski network of complete graph Kk. In addition, we will also determine the b-choromatic number of Sierpinski gasket graph S(n). As an application, we will also determine the b-chromatic number of Sierpinski graph of house graph.
{"title":"The study of the b-choromatic number of some classes of fractal graphs","authors":"Tayyiba Sattar, M. S. Sardar, M. Alaeiyan, M. R. Farahani, M. Cancan, Ziyattin Taş","doi":"10.1080/09720529.2022.2067390","DOIUrl":"https://doi.org/10.1080/09720529.2022.2067390","url":null,"abstract":"Abstract In graph coloring, labels are assigned to graph elements according to certain constraints. Colors are a special case of graph labeling as well as in practical applications, graph coloring also poses some theoretical challenges. A topic related to graph coloring will be discussed in this study, i.e., b-chromatic number. In proper coloring, edges, vertices, or both of them are colored so that they are distinct from one another. A b-coloring of m colors of a graph G is similar to proper coloring in which at least one vertex from each color class is connected to (m-1) other colors. The b-chromatic number of a graph G is the greatest positive number k such that G admits a b-coloring with k colors and is represented by ϕ(G). Fractals are geometric objects that are self-similar at multiple scales and their geometric measurements are different from fractal measurements. In this paper, we will evaluate the b-chromatic number of Fractal type graphs, i.e., Sierpinski network S(n; Kk) (where Kk is a complete graph of order k) and Sierpinski gasket network S(n). Firstly, we will compute the b-chromatic number of S(n; K3), S(n; K4) and S(n; K5) for n ≥ 2. After that, we will generalize the result for the Sierpinski network of complete graph Kk. In addition, we will also determine the b-choromatic number of Sierpinski gasket graph S(n). As an application, we will also determine the b-chromatic number of Sierpinski graph of house graph.","PeriodicalId":46563,"journal":{"name":"JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY","volume":"25 1","pages":"1509 - 1524"},"PeriodicalIF":1.4,"publicationDate":"2022-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48361965","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 : 2022-05-31DOI: 10.1080/09720529.2022.2068599
Hassanein Falah, Sarah Nahed Abdul Abbas
Abstract In this paper, authors defined a conical open set’s characterization. As a consequence, they introduced the (- space and - space)-open subdigraph in graph theory. Their interrelationships were investigated. As a result, several theorems have been proven. The aim of this paper, is to find graph theory applications due to the difficulty in finding applications in topological spaces, which are pure mathematics branches. We defined a conical open set’s characterization. As a consequence, we introduced the ( space and - space )-open subdigraph in graph theory. Their interrelationships were investigated. As a result, several theorems have been proven.
{"title":"Characterization of α-open set and α-closure operator via digraph","authors":"Hassanein Falah, Sarah Nahed Abdul Abbas","doi":"10.1080/09720529.2022.2068599","DOIUrl":"https://doi.org/10.1080/09720529.2022.2068599","url":null,"abstract":"Abstract In this paper, authors defined a conical open set’s characterization. As a consequence, they introduced the (- space and - space)-open subdigraph in graph theory. Their interrelationships were investigated. As a result, several theorems have been proven. The aim of this paper, is to find graph theory applications due to the difficulty in finding applications in topological spaces, which are pure mathematics branches. We defined a conical open set’s characterization. As a consequence, we introduced the ( space and - space )-open subdigraph in graph theory. Their interrelationships were investigated. As a result, several theorems have been proven.","PeriodicalId":46563,"journal":{"name":"JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY","volume":"25 1","pages":"1475 - 1485"},"PeriodicalIF":1.4,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45308437","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 : 2022-05-24DOI: 10.1080/09720529.2021.2020427
Asmaa Boudali, N. H. Said, A. Ali-Pacha
Abstract Multimedia data including text, audio, image, and video are increasingly transmitted over networks or stored in digital format. Therefore, secure transmission and storage are required to preserve it. This is why the utilization of cryptography has become imperative to establish new approaches for rising security. The cryptographic systems rely on cellular automata (CA) and chaotic systems, which are fundamental in various cryptographic applications such as key generation and image encryption. Some of them are complex and others have little key space. In this paper, a novel research work based on cellular automata and chaotic logistic mapping is proposed. Overall, the paper aims to propose a new cryptographic system that produces encrypted data with random characteristics. A novel technique is adopted to develop the evolution of configurations in elementary cellular automata (ECA) which makes the obtained result more random. Simulation results demonstrate that the proposed approach has a high level of security and resists various attacks. In addition, it outperforms some existing image encryption algorithms.
{"title":"A new symmetrical cryptosystem based cellular automata and chaotic map function","authors":"Asmaa Boudali, N. H. Said, A. Ali-Pacha","doi":"10.1080/09720529.2021.2020427","DOIUrl":"https://doi.org/10.1080/09720529.2021.2020427","url":null,"abstract":"Abstract Multimedia data including text, audio, image, and video are increasingly transmitted over networks or stored in digital format. Therefore, secure transmission and storage are required to preserve it. This is why the utilization of cryptography has become imperative to establish new approaches for rising security. The cryptographic systems rely on cellular automata (CA) and chaotic systems, which are fundamental in various cryptographic applications such as key generation and image encryption. Some of them are complex and others have little key space. In this paper, a novel research work based on cellular automata and chaotic logistic mapping is proposed. Overall, the paper aims to propose a new cryptographic system that produces encrypted data with random characteristics. A novel technique is adopted to develop the evolution of configurations in elementary cellular automata (ECA) which makes the obtained result more random. Simulation results demonstrate that the proposed approach has a high level of security and resists various attacks. In addition, it outperforms some existing image encryption algorithms.","PeriodicalId":46563,"journal":{"name":"JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY","volume":"25 1","pages":"1435 - 1455"},"PeriodicalIF":1.4,"publicationDate":"2022-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43337523","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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