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(k,ℓ) - kernels in the Generalised Mycielskian of Digraphs 广义有向图Mycielskian的(k, r) -核
Discrete Mathematics Algorithms and Applications Pub Date : 2023-10-20 DOI: 10.1142/s1793830923500933
R. Lakshmi, D. G. Sindhu
{"title":"(<i>k</i>,ℓ) - kernels in the Generalised Mycielskian of Digraphs","authors":"R. Lakshmi, D. G. Sindhu","doi":"10.1142/s1793830923500933","DOIUrl":"https://doi.org/10.1142/s1793830923500933","url":null,"abstract":"","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"75 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135567055","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}
引用次数: 0
An algorithm for the domination number and neighbor-component order connectivity of a unicycle 一种独轮车支配数和邻元阶连通性的算法
Discrete Mathematics Algorithms and Applications Pub Date : 2023-10-20 DOI: 10.1142/s1793830923500945
Kristi Luttrell
{"title":"An algorithm for the domination number and neighbor-component order connectivity of a unicycle","authors":"Kristi Luttrell","doi":"10.1142/s1793830923500945","DOIUrl":"https://doi.org/10.1142/s1793830923500945","url":null,"abstract":"","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"81 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135566813","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}
引用次数: 0
Local Multiset Dimension of Corona Product on Tree Graphs 树形图上电晕积的局部多集维
Discrete Mathematics Algorithms and Applications Pub Date : 2023-10-20 DOI: 10.1142/s1793830923500921
Ridho Alfarisi, Liliek Susilowati, None Dafik, Arika Indah Kristiana
{"title":"Local Multiset Dimension of Corona Product on Tree Graphs","authors":"Ridho Alfarisi, Liliek Susilowati, None Dafik, Arika Indah Kristiana","doi":"10.1142/s1793830923500921","DOIUrl":"https://doi.org/10.1142/s1793830923500921","url":null,"abstract":"","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135567078","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}
引用次数: 0
The 3-forced 2-structures 3-强制2-结构
Discrete Mathematics Algorithms and Applications Pub Date : 2023-10-18 DOI: 10.1142/s1793830923500866
Abderrahim Boussairi, Pierre Ille
{"title":"The 3-forced 2-structures","authors":"Abderrahim Boussairi, Pierre Ille","doi":"10.1142/s1793830923500866","DOIUrl":"https://doi.org/10.1142/s1793830923500866","url":null,"abstract":"Given sets [Formula: see text] and [Formula: see text], a labeled 2-structure is a function [Formula: see text] from [Formula: see text] to [Formula: see text]. The set [Formula: see text] is called the vertex set of [Formula: see text] and denoted by [Formula: see text]. The label set of [Formula: see text] is the set [Formula: see text] of [Formula: see text] such that [Formula: see text] for some [Formula: see text]. Given [Formula: see text], the 2-substructure [Formula: see text] of [Formula: see text] is denoted by [Formula: see text]. The dual [Formula: see text] of [Formula: see text] is defined on [Formula: see text] as follows. For distinct [Formula: see text], [Formula: see text]. A labeled 2-Structure [Formula: see text] is reversible provided that for [Formula: see text] such that [Formula: see text] and [Formula: see text], if [Formula: see text], then [Formula: see text]. We only consider reversible labeled 2-structures whose vertex set is finite. Let [Formula: see text] and [Formula: see text] be 2-structures such that [Formula: see text]. Given [Formula: see text], [Formula: see text] and [Formula: see text] are [Formula: see text]-hemimorphic if for every [Formula: see text] such that [Formula: see text], [Formula: see text] is isomorphic to [Formula: see text] or [Formula: see text]. Furthermore, let [Formula: see text] be a 2-structure. Given [Formula: see text], [Formula: see text] is [Formula: see text]-forced if [Formula: see text] and [Formula: see text] are the only 2-structures [Formula: see text]-hemimorphic to [Formula: see text]. We characterize the [Formula: see text]-forced 2-structures. Last, we provide a large class of [Formula: see text]-forced 2-structures.","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135823139","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}
引用次数: 0
Further results on independent edge-vertex domination 关于边-顶点独立支配的进一步结果
Discrete Mathematics Algorithms and Applications Pub Date : 2023-10-18 DOI: 10.1142/s1793830923500805
Mustapha Chellali
{"title":"Further results on independent edge-vertex domination","authors":"Mustapha Chellali","doi":"10.1142/s1793830923500805","DOIUrl":"https://doi.org/10.1142/s1793830923500805","url":null,"abstract":"Given a graph [Formula: see text] with no isolated vertices, let [Formula: see text] [Formula: see text] [Formula: see text] [Formula: see text] [Formula: see text] and [Formula: see text] denote the ev-domination number, the independent ev-domination number, the upper independent ev-domination number, the domination number, the paired-domination number and the upper paired-domination number, respectively. It is known that [Formula: see text] In this paper, we extend this inequality chain to involve the upper paired-domination number for arbitrary graphs [Formula: see text] with no isolated vertices as well as the domination number for trees. Moreover, we show that recognizing well ev-covered graphs (i.e., graphs [Formula: see text] with [Formula: see text]) is co-NP-complete, solving an open problem posed by Boutrig and Chellali.","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"140 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135823302","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}
引用次数: 0
Fair Detour Domination of Graphs 图的公平迂回支配
Discrete Mathematics Algorithms and Applications Pub Date : 2023-10-17 DOI: 10.1142/s1793830923500830
J. Vijaya Xavier Parthipan, D. Jeba Ebenezer
{"title":"Fair Detour Domination of Graphs","authors":"J. Vijaya Xavier Parthipan, D. Jeba Ebenezer","doi":"10.1142/s1793830923500830","DOIUrl":"https://doi.org/10.1142/s1793830923500830","url":null,"abstract":"A set [Formula: see text] of a connected graph [Formula: see text] is called a fair detour dominating set if D is a detour dominating set and every two vertices not in D has same number of neighbors in D. The fair detour domination number, [Formula: see text], of G is the minimum cardinality of fair detour dominating sets. A fair detour dominating set of cardinality [Formula: see text] is called a [Formula: see text]-set of G. The fair detour domination number of some well-known graphs are determined. We have shown that, If G is a connected graph with [Formula: see text] and [Formula: see text] then [Formula: see text]. It is shown that for given positive integers [Formula: see text], [Formula: see text], [Formula: see text] such that [Formula: see text] there exists a connected graph G of order [Formula: see text] such that [Formula: see text] and [Formula: see text].","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944600","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}
引用次数: 0
Hamilton cycles in Generalized Mycielski Graphs 广义Mycielski图中的Hamilton环
Discrete Mathematics Algorithms and Applications Pub Date : 2023-10-17 DOI: 10.1142/s179383092350088x
L. Panneerselvam, S. Ganesamurthy, A. Muthusamy
{"title":"Hamilton cycles in Generalized Mycielski Graphs","authors":"L. Panneerselvam, S. Ganesamurthy, A. Muthusamy","doi":"10.1142/s179383092350088x","DOIUrl":"https://doi.org/10.1142/s179383092350088x","url":null,"abstract":"Let [Formula: see text] denote the generalized Mycielski graph of [Formula: see text]. In this paper, it is proved that for [Formula: see text], if [Formula: see text] has [Formula: see text] pairwise edge-disjoint Hamilton cycles, then [Formula: see text] has [Formula: see text] Hamilton cycles which are pairwise edge-disjoint. Further, it is shown that if [Formula: see text] has [Formula: see text] pairwise edge-disjoint Hamilton cycles with [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text], then [Formula: see text] has [Formula: see text] pairwise edge-disjoint Hamilton cycles. Finally it is shown that [Formula: see text] is hamiltonian even when [Formula: see text] is non-hamiltonian with a specified [Formula: see text]-factor. Consequently, the Mycielski graph of Flower Snark graph [Formula: see text], for all odd [Formula: see text], is Hamiltonian.","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"268 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944286","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}
引用次数: 0
On Metric Dimension of Nil-Graph of Ideals of Commutative Rings 交换环理想的零图的度量维数
Discrete Mathematics Algorithms and Applications Pub Date : 2023-10-14 DOI: 10.1142/s1793830923500787
K. Selvakumar, N. Petchiammal
{"title":"On Metric Dimension of Nil-Graph of Ideals of Commutative Rings","authors":"K. Selvakumar, N. Petchiammal","doi":"10.1142/s1793830923500787","DOIUrl":"https://doi.org/10.1142/s1793830923500787","url":null,"abstract":"Let [Formula: see text] be a commutative ring with identity and [Formula: see text] be the ideal of all nilpotent elements of [Formula: see text]. Let [Formula: see text] be a nontrivial ideal of [Formula: see text] and there exists a nontrivial ideal [Formula: see text] such that [Formula: see text] The nil-graph of ideals of [Formula: see text] is defined as the graph [Formula: see text] whose vertex set is the set [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. A subset of vertices [Formula: see text] resolves a graph [Formula: see text] and [Formula: see text] is a resolving set of [Formula: see text] if every vertex is uniquely determined by its vector of distances to the vertices of [Formula: see text] In particular, for an ordered subset [Formula: see text] of vertices in a connected graph [Formula: see text] and a vertex [Formula: see text] of [Formula: see text] the metric representation of [Formula: see text] with respect to [Formula: see text] is the [Formula: see text]-vector [Formula: see text] The set [Formula: see text] is a resolving set for [Formula: see text] if [Formula: see text] implies that [Formula: see text] for all pair of vertices, [Formula: see text] A resolving set [Formula: see text] of minimum cardinality is the metric basis for [Formula: see text] and the number of elements in the resolving set of minimum cardinality is the metric dimension of [Formula: see text] If [Formula: see text] for every pair [Formula: see text] of adjacent vertices of [Formula: see text] then [Formula: see text] is called a local metric set of [Formula: see text]. The minimum [Formula: see text] for which [Formula: see text] has a local metric [Formula: see text]-set is the local metric dimension of [Formula: see text] which is denoted by [Formula: see text]. In this paper, we determine metric dimension and local metric dimension of nil-graph of ideals of commutative rings.","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135767364","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}
引用次数: 0
On the Classification of Codes over Non-Unital Ring of Order 4 关于4阶非酉环上码的分类
Discrete Mathematics Algorithms and Applications Pub Date : 2023-10-14 DOI: 10.1142/s1793830923500763
Sourav Deb, Isha Kikani, Manish K. Gupta
{"title":"On the Classification of Codes over Non-Unital Ring of Order 4","authors":"Sourav Deb, Isha Kikani, Manish K. Gupta","doi":"10.1142/s1793830923500763","DOIUrl":"https://doi.org/10.1142/s1793830923500763","url":null,"abstract":"In the last 60 years coding theory has been studied a lot over finite fields [Formula: see text] or commutative rings [Formula: see text] with unity. Although in [Formula: see text], a study on the classification of the rings (not necessarily commutative or ring with unity) of order [Formula: see text] had been presented, the construction of codes over non-commutative rings or non-commutative non-unital rings surfaced merely two years ago. In this letter, we extend the diverse research on exploring the codes over the non-commutative and non-unital ring [Formula: see text] by presenting the classification of optimal and nice codes of length [Formula: see text] over [Formula: see text], along with respective weight enumerators and complete weight enumerators.","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135767359","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}
引用次数: 0
Classification of a Class of A3MDS Code and Applications in Secret-Sharing Schemes 一类A3MDS代码的分类及其在秘密共享方案中的应用
Discrete Mathematics Algorithms and Applications Pub Date : 2023-10-14 DOI: 10.1142/s1793830923500842
Bandana Pandey, Prabal Paul
{"title":"Classification of a Class of <i>A</i><sup>3</sup><i>MDS</i> Code and Applications in Secret-Sharing Schemes","authors":"Bandana Pandey, Prabal Paul","doi":"10.1142/s1793830923500842","DOIUrl":"https://doi.org/10.1142/s1793830923500842","url":null,"abstract":"A [Formula: see text]-ary linear [Formula: see text] code [Formula: see text] is known as [Formula: see text] code. If [Formula: see text] the code is called a maximum distance separable code. [Formula: see text] codes are known to be useful in the secret-sharing schemes and coding theory. In this paper, we classify all binary self-orthogonal [Formula: see text] codes. We have introduced a subclass of [Formula: see text] codes, called [Formula: see text] codes, to form a special type of secret-sharing scheme where for any participant, there exist [Formula: see text] other participants who can collectively reveal the secret by combining their shares and there exists another set of [Formula: see text] participants including the given participant, who cannot reveal the secret.","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135767367","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}
引用次数: 0
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