Pub Date : 2023-10-14DOI: 10.1142/s1793830923500829
P. Roushini Leely Pushpam, K. Priya Bhanthavi
A set [Formula: see text] of vertices in a graph [Formula: see text] is called a dominating set if every vertex in [Formula: see text] is adjacent to a vertex in [Formula: see text]. Hamid defined a dominating set which intersects every maximum independent set in [Formula: see text] to be an independent transversal dominating set. The minimum cardinality of an independent transversal dominating set is called the independent transversal domination number of [Formula: see text] and is denoted by [Formula: see text]. In this paper we prove that for trees [Formula: see text], [Formula: see text] is bounded above by [Formula: see text] and characterize the extremal trees. Further, we characterize the class of all trees whose independent transversal domination number does not alter owing to the deletion of an edge.
{"title":"More on independent transversal domination","authors":"P. Roushini Leely Pushpam, K. Priya Bhanthavi","doi":"10.1142/s1793830923500829","DOIUrl":"https://doi.org/10.1142/s1793830923500829","url":null,"abstract":"A set [Formula: see text] of vertices in a graph [Formula: see text] is called a dominating set if every vertex in [Formula: see text] is adjacent to a vertex in [Formula: see text]. Hamid defined a dominating set which intersects every maximum independent set in [Formula: see text] to be an independent transversal dominating set. The minimum cardinality of an independent transversal dominating set is called the independent transversal domination number of [Formula: see text] and is denoted by [Formula: see text]. In this paper we prove that for trees [Formula: see text], [Formula: see text] is bounded above by [Formula: see text] and characterize the extremal trees. Further, we characterize the class of all trees whose independent transversal domination number does not alter owing to the deletion of an edge.","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"32 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":"135767366","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 : 2023-10-06DOI: 10.1142/s1793830923500817
S. Anandha Prabhavathy, I. Sahul Hamid
A majority double Roman dominating function (MDRDF) on a graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex [Formula: see text] with [Formula: see text] is adjacent to at least two vertices assigned with 2 or to at least one vertex [Formula: see text] with [Formula: see text], (ii) every vertex [Formula: see text] with [Formula: see text] is adjacent to at least one vertex [Formula: see text] with [Formula: see text] and (iii) [Formula: see text], for at least half of the vertices in [Formula: see text]. The weight of an MDRDF is the sum of its function values over all vertices. The majority double Roman domination number of a graph [Formula: see text], denoted by [Formula: see text], is defined as [Formula: see text]. In this paper, we introduce and study the majority double Roman domination number on some classes of graphs.
{"title":"Majority double Roman domination in graphs","authors":"S. Anandha Prabhavathy, I. Sahul Hamid","doi":"10.1142/s1793830923500817","DOIUrl":"https://doi.org/10.1142/s1793830923500817","url":null,"abstract":"A majority double Roman dominating function (MDRDF) on a graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex [Formula: see text] with [Formula: see text] is adjacent to at least two vertices assigned with 2 or to at least one vertex [Formula: see text] with [Formula: see text], (ii) every vertex [Formula: see text] with [Formula: see text] is adjacent to at least one vertex [Formula: see text] with [Formula: see text] and (iii) [Formula: see text], for at least half of the vertices in [Formula: see text]. The weight of an MDRDF is the sum of its function values over all vertices. The majority double Roman domination number of a graph [Formula: see text], denoted by [Formula: see text], is defined as [Formula: see text]. In this paper, we introduce and study the majority double Roman domination number on some classes of graphs.","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135302897","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 : 2023-09-29DOI: 10.1142/s1793830923300035
S. Madhumitha, Sudev Naduvath
{"title":"Graphs on groups in terms of the order of elements: A Review","authors":"S. Madhumitha, Sudev Naduvath","doi":"10.1142/s1793830923300035","DOIUrl":"https://doi.org/10.1142/s1793830923300035","url":null,"abstract":"","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"220 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135192653","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 : 2023-09-27DOI: 10.1142/s1793830923500726
Swati Bhardwaj, Mokshi Goyal, Madhu Raka
Let [Formula: see text] be a prime power and let [Formula: see text] be a finite non-chain ring, where [Formula: see text], are polynomials, not all linear, which split into distinct linear factors over [Formula: see text]. We characterize constacyclic codes over the ring [Formula: see text] and study quantum codes from these. As an application, some new and better quantum codes, as compared to the best known codes, are obtained. We also prove that the choice of the polynomials [Formula: see text], [Formula: see text], is irrelevant while constructing quantum codes from constacyclic codes over [Formula: see text], it depends only on their degrees.
{"title":"New quantum codes from constacyclic codes over a general non-chain ring","authors":"Swati Bhardwaj, Mokshi Goyal, Madhu Raka","doi":"10.1142/s1793830923500726","DOIUrl":"https://doi.org/10.1142/s1793830923500726","url":null,"abstract":"Let [Formula: see text] be a prime power and let [Formula: see text] be a finite non-chain ring, where [Formula: see text], are polynomials, not all linear, which split into distinct linear factors over [Formula: see text]. We characterize constacyclic codes over the ring [Formula: see text] and study quantum codes from these. As an application, some new and better quantum codes, as compared to the best known codes, are obtained. We also prove that the choice of the polynomials [Formula: see text], [Formula: see text], is irrelevant while constructing quantum codes from constacyclic codes over [Formula: see text], it depends only on their degrees.","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135475919","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 : 2023-09-26DOI: 10.1142/s1793830923500799
Zeynep Nihan Berberler
The entropy of a graph is an information-theoretic quantity which expresses the complexity of a graph. Entropy functions have been used successfully to capture different aspects of graph complexity. The generalized graph entropies result from applying information measures to a graph using various schemes for defining probability distributions over the elements of the graph. In this paper, we investigate the complexity of a class of composite graphs based on subdivision graphs and corona product evaluating the generalized graph entropies, and we present explicit formulae for the complexity of subdivision-corona type product graphs.
{"title":"Generalized Entropies of Subdivision-Corona Networks","authors":"Zeynep Nihan Berberler","doi":"10.1142/s1793830923500799","DOIUrl":"https://doi.org/10.1142/s1793830923500799","url":null,"abstract":"The entropy of a graph is an information-theoretic quantity which expresses the complexity of a graph. Entropy functions have been used successfully to capture different aspects of graph complexity. The generalized graph entropies result from applying information measures to a graph using various schemes for defining probability distributions over the elements of the graph. In this paper, we investigate the complexity of a class of composite graphs based on subdivision graphs and corona product evaluating the generalized graph entropies, and we present explicit formulae for the complexity of subdivision-corona type product graphs.","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134903939","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 : 2023-08-30DOI: 10.1142/s1793830923500775
V. Keerthika, G. Muhiuddin, D. Al-Kadi, B. Elavarasan
{"title":"Hybrid norm structures applied to hemirings","authors":"V. Keerthika, G. Muhiuddin, D. Al-Kadi, B. Elavarasan","doi":"10.1142/s1793830923500775","DOIUrl":"https://doi.org/10.1142/s1793830923500775","url":null,"abstract":"","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"10 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89624030","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 : 2023-08-24DOI: 10.1142/s179383092350074x
Sang-Eon Han
{"title":"DT-k-Group Structures on Digital Objects and an Answer to an Open Problem","authors":"Sang-Eon Han","doi":"10.1142/s179383092350074x","DOIUrl":"https://doi.org/10.1142/s179383092350074x","url":null,"abstract":"","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"52 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90995528","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 : 2023-08-17DOI: 10.1142/s1793830923500714
Yangjiang Wei, Y. Zou
{"title":"Study Boolean Networks via Matrices of Support","authors":"Yangjiang Wei, Y. Zou","doi":"10.1142/s1793830923500714","DOIUrl":"https://doi.org/10.1142/s1793830923500714","url":null,"abstract":"","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"40 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78548440","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 : 2023-08-17DOI: 10.1142/s1793830923500738
Vikram Srinivasan Thiru, S. Balaji
{"title":"Strong Chromatic Indices of certain Binary operations on graphs","authors":"Vikram Srinivasan Thiru, S. Balaji","doi":"10.1142/s1793830923500738","DOIUrl":"https://doi.org/10.1142/s1793830923500738","url":null,"abstract":"","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"6 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72696777","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 : 2023-08-17DOI: 10.1142/s1793830923500593
Mohammad Alzohairi, Tarak Louleb, Mohamed Y. Sayar
In a graph [Formula: see text], a subset [Formula: see text] of the vertex set [Formula: see text] is a module (or interval, clan) of [Formula: see text] if every vertex outside [Formula: see text] is adjacent to all or none of [Formula: see text]. The empty set, the singleton sets, and the full set of vertices are trivial modules. The graph [Formula: see text] is indecomposable (or prime) if all its modules are trivial. If [Formula: see text] is indecomposable, we say that an edge [Formula: see text] of [Formula: see text] is a removable edge if [Formula: see text] is indecomposable (here [Formula: see text]). The graph [Formula: see text] is said to be unstable if it has no removable edges. For a positive integer [Formula: see text], the [Formula: see text]th power [Formula: see text] of a graph [Formula: see text] is the graph obtained from [Formula: see text] by adding an edge between all pairs of vertices of [Formula: see text] with distance at most [Formula: see text]. A graph [Formula: see text] of order [Formula: see text] (i.e., [Formula: see text]) is said to be [Formula: see text]-placeable into [Formula: see text], if [Formula: see text] contains [Formula: see text] edge-disjoint copies of [Formula: see text]. In this paper, we answer a question, suggested by Boudabbous in a personal communication, concerning unstable graphs and packing into their fifth power as follows: First, we give a characterization of the unstable graphs which is deduced from the results given by Ehrenfeucht, Harju and Rozenberg (the theory of [Formula: see text]-structures: a framework for decomposition and transformation of graphs). Second, we prove that every unstable graph [Formula: see text] is [Formula: see text]-placeable into [Formula: see text].
{"title":"Unstable graphs and packing into fifth power","authors":"Mohammad Alzohairi, Tarak Louleb, Mohamed Y. Sayar","doi":"10.1142/s1793830923500593","DOIUrl":"https://doi.org/10.1142/s1793830923500593","url":null,"abstract":"In a graph [Formula: see text], a subset [Formula: see text] of the vertex set [Formula: see text] is a module (or interval, clan) of [Formula: see text] if every vertex outside [Formula: see text] is adjacent to all or none of [Formula: see text]. The empty set, the singleton sets, and the full set of vertices are trivial modules. The graph [Formula: see text] is indecomposable (or prime) if all its modules are trivial. If [Formula: see text] is indecomposable, we say that an edge [Formula: see text] of [Formula: see text] is a removable edge if [Formula: see text] is indecomposable (here [Formula: see text]). The graph [Formula: see text] is said to be unstable if it has no removable edges. For a positive integer [Formula: see text], the [Formula: see text]th power [Formula: see text] of a graph [Formula: see text] is the graph obtained from [Formula: see text] by adding an edge between all pairs of vertices of [Formula: see text] with distance at most [Formula: see text]. A graph [Formula: see text] of order [Formula: see text] (i.e., [Formula: see text]) is said to be [Formula: see text]-placeable into [Formula: see text], if [Formula: see text] contains [Formula: see text] edge-disjoint copies of [Formula: see text]. In this paper, we answer a question, suggested by Boudabbous in a personal communication, concerning unstable graphs and packing into their fifth power as follows: First, we give a characterization of the unstable graphs which is deduced from the results given by Ehrenfeucht, Harju and Rozenberg (the theory of [Formula: see text]-structures: a framework for decomposition and transformation of graphs). Second, we prove that every unstable graph [Formula: see text] is [Formula: see text]-placeable into [Formula: see text].","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88602568","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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