Pub Date : 2023-11-10DOI: 10.1142/s1793830923500994
T. P. Sandhiya, J. Geetha, K. Somasundaram
{"title":"Total Chromatic Number for Certain Classes of Product Graphs","authors":"T. P. Sandhiya, J. Geetha, K. Somasundaram","doi":"10.1142/s1793830923500994","DOIUrl":"https://doi.org/10.1142/s1793830923500994","url":null,"abstract":"","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":" 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135191288","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 : 2023-11-10DOI: 10.1142/s1793830923300047
Guanghua Wang, Weili Wu
{"title":"Surveying the Landscape of Text Summarization with Deep Learning: A Comprehensive Review","authors":"Guanghua Wang, Weili Wu","doi":"10.1142/s1793830923300047","DOIUrl":"https://doi.org/10.1142/s1793830923300047","url":null,"abstract":"","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":" June","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135186019","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 : 2023-11-04DOI: 10.1142/s1793830923500891
Y. Therese Sunitha Mary, R. Kala
The strong nonsplit domsaturation number of a graph [Formula: see text], [Formula: see text] is the least positive integer [Formula: see text] such that every vertex of [Formula: see text] lies in a strong nonsplit dominating set of cardinality [Formula: see text]. In this paper, we obtain certain bounds for [Formula: see text] and characterize the graphs which attain these bounds.
{"title":"Strong Nonsplit domsaturation number of a graph","authors":"Y. Therese Sunitha Mary, R. Kala","doi":"10.1142/s1793830923500891","DOIUrl":"https://doi.org/10.1142/s1793830923500891","url":null,"abstract":"The strong nonsplit domsaturation number of a graph [Formula: see text], [Formula: see text] is the least positive integer [Formula: see text] such that every vertex of [Formula: see text] lies in a strong nonsplit dominating set of cardinality [Formula: see text]. In this paper, we obtain certain bounds for [Formula: see text] and characterize the graphs which attain these bounds.","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"14 11","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135728299","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 : 2023-11-02DOI: 10.1142/s1793830923500878
S. Visweswaran
The rings considered in this paper are commutative with identity which are not integral domains. Let [Formula: see text] be a ring. An ideal [Formula: see text] of [Formula: see text] is said to be an annihilating ideal if there exists [Formula: see text] such that [Formula: see text]. Let [Formula: see text] denote the set of all annihilating ideals of [Formula: see text] and we denote [Formula: see text] by [Formula: see text]. With [Formula: see text], in this paper, we associate an undirected graph denoted by [Formula: see text] whose vertex set is [Formula: see text] and two distinct vertices [Formula: see text] are adjacent in this graph if and only if either [Formula: see text] or [Formula: see text]. The aim of this paper is to study the interplay between some graph properties of [Formula: see text] and the algebraic properties of [Formula: see text] and to compare some graph properties of [Formula: see text] with the corresponding graph properties of the annihilating ideal graph of [Formula: see text] and the sum annihilating ideal graph of [Formula: see text].
{"title":"Some results on a supergraph of the sum annihilating ideal graph of a commutative ring","authors":"S. Visweswaran","doi":"10.1142/s1793830923500878","DOIUrl":"https://doi.org/10.1142/s1793830923500878","url":null,"abstract":"The rings considered in this paper are commutative with identity which are not integral domains. Let [Formula: see text] be a ring. An ideal [Formula: see text] of [Formula: see text] is said to be an annihilating ideal if there exists [Formula: see text] such that [Formula: see text]. Let [Formula: see text] denote the set of all annihilating ideals of [Formula: see text] and we denote [Formula: see text] by [Formula: see text]. With [Formula: see text], in this paper, we associate an undirected graph denoted by [Formula: see text] whose vertex set is [Formula: see text] and two distinct vertices [Formula: see text] are adjacent in this graph if and only if either [Formula: see text] or [Formula: see text]. The aim of this paper is to study the interplay between some graph properties of [Formula: see text] and the algebraic properties of [Formula: see text] and to compare some graph properties of [Formula: see text] with the corresponding graph properties of the annihilating ideal graph of [Formula: see text] and the sum annihilating ideal graph of [Formula: see text].","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"64 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135874437","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 : 2023-11-01DOI: 10.1142/s1793830923500982
B. J. Septory, L. Susilowati, None Dafik, M. Venkatachalam
{"title":"On the study of rainbow antimagic connection number of comb product of tree and complete bipartite graph","authors":"B. J. Septory, L. Susilowati, None Dafik, M. Venkatachalam","doi":"10.1142/s1793830923500982","DOIUrl":"https://doi.org/10.1142/s1793830923500982","url":null,"abstract":"","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135216208","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 : 2023-10-31DOI: 10.1142/s1793830923500908
S. M. Hegde, Lolita Priya Castelino
Let [Formula: see text] be a directed graph with [Formula: see text] vertices and [Formula: see text] arcs. A function [Formula: see text] where [Formula: see text] is called a complete coloring of [Formula: see text] if and only if for every arc [Formula: see text] of [Formula: see text], the ordered pair [Formula: see text] appears at least once. If the pair [Formula: see text] is not assigned, then [Formula: see text] is called a [Formula: see text] [Formula: see text] [Formula: see text] of [Formula: see text]. The maximum [Formula: see text] for which [Formula: see text] admits a proper complete coloring is called the [Formula: see text] [Formula: see text] of [Formula: see text] and is denoted by [Formula: see text]. We obtain the upper bound for the achromatic number of digraphs and regular digraphs and investigate the same for some classes of digraphs such as unipath, unicycle, circulant digraphs, etc.
{"title":"Achromatic Number of Some Classes of Digraphs","authors":"S. M. Hegde, Lolita Priya Castelino","doi":"10.1142/s1793830923500908","DOIUrl":"https://doi.org/10.1142/s1793830923500908","url":null,"abstract":"Let [Formula: see text] be a directed graph with [Formula: see text] vertices and [Formula: see text] arcs. A function [Formula: see text] where [Formula: see text] is called a complete coloring of [Formula: see text] if and only if for every arc [Formula: see text] of [Formula: see text], the ordered pair [Formula: see text] appears at least once. If the pair [Formula: see text] is not assigned, then [Formula: see text] is called a [Formula: see text] [Formula: see text] [Formula: see text] of [Formula: see text]. The maximum [Formula: see text] for which [Formula: see text] admits a proper complete coloring is called the [Formula: see text] [Formula: see text] of [Formula: see text] and is denoted by [Formula: see text]. We obtain the upper bound for the achromatic number of digraphs and regular digraphs and investigate the same for some classes of digraphs such as unipath, unicycle, circulant digraphs, etc.","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"364 13","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135765192","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 : 2023-10-31DOI: 10.1142/s1793830923500854
Leonard M. Paleta, Ferdinand P. Jamil
For a vertex [Formula: see text] in a simple, finite and undirected graph [Formula: see text], the neighborhood [Formula: see text] of [Formula: see text] is the set consisting of all vertices of [Formula: see text] which are adjacent to [Formula: see text]. A perfect Italian dominating function on [Formula: see text] is a function [Formula: see text] such that for each [Formula: see text] with [Formula: see text], [Formula: see text]. The weight of a perfect Italian dominating function [Formula: see text] is the value [Formula: see text]. The perfect Italian domination number of [Formula: see text] is the minimum weight of a perfect Italian dominating function on [Formula: see text]. In this paper, we study the perfect Italian domination in graphs under some binary operations.
{"title":"On perfect Italian domination in graphs","authors":"Leonard M. Paleta, Ferdinand P. Jamil","doi":"10.1142/s1793830923500854","DOIUrl":"https://doi.org/10.1142/s1793830923500854","url":null,"abstract":"For a vertex [Formula: see text] in a simple, finite and undirected graph [Formula: see text], the neighborhood [Formula: see text] of [Formula: see text] is the set consisting of all vertices of [Formula: see text] which are adjacent to [Formula: see text]. A perfect Italian dominating function on [Formula: see text] is a function [Formula: see text] such that for each [Formula: see text] with [Formula: see text], [Formula: see text]. The weight of a perfect Italian dominating function [Formula: see text] is the value [Formula: see text]. The perfect Italian domination number of [Formula: see text] is the minimum weight of a perfect Italian dominating function on [Formula: see text]. In this paper, we study the perfect Italian domination in graphs under some binary operations.","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"34 31","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135765496","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 : 2023-10-27DOI: 10.1142/s1793830923500969
Rahul Kumar Gautam, Anjeneya Swami Kare, S. Durga Bhavani
{"title":"Approximation Algorithms for the Graph Burning on Cactus and Directed Trees","authors":"Rahul Kumar Gautam, Anjeneya Swami Kare, S. Durga Bhavani","doi":"10.1142/s1793830923500969","DOIUrl":"https://doi.org/10.1142/s1793830923500969","url":null,"abstract":"","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136312432","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 : 2023-10-27DOI: 10.1142/s1793830923500970
A. I. Kristiana, D. Setyawan, R. Alfarisi, R. M. Prihandini
{"title":"On Graceful Coloring of Generalized Petersen Graphs","authors":"A. I. Kristiana, D. Setyawan, R. Alfarisi, R. M. Prihandini","doi":"10.1142/s1793830923500970","DOIUrl":"https://doi.org/10.1142/s1793830923500970","url":null,"abstract":"","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136312418","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 : 2023-10-27DOI: 10.1142/s1793830923500957
Maria Andrea O. Bonsocan, Ferdinand P. Jamil
{"title":"Transversal Total Hop Domination in Graphs","authors":"Maria Andrea O. Bonsocan, Ferdinand P. Jamil","doi":"10.1142/s1793830923500957","DOIUrl":"https://doi.org/10.1142/s1793830923500957","url":null,"abstract":"","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136312440","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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