Pub Date : 2024-01-19DOI: 10.1142/s1793830924500095
Soumen Pradhan, S. Kar, B. Biswas
{"title":"Independence and domination number of order two element graph over a group","authors":"Soumen Pradhan, S. Kar, B. Biswas","doi":"10.1142/s1793830924500095","DOIUrl":"https://doi.org/10.1142/s1793830924500095","url":null,"abstract":"","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139525545","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 : 2024-01-10DOI: 10.1142/s1793830923501203
Saraswati Bajaj, P. Panigrahi
For a finite simple undirected graph [Formula: see text], the universal adjacency matrix [Formula: see text] is a linear combination of the adjacency matrix [Formula: see text], the degree diagonal matrix [Formula: see text], the identity matrix [Formula: see text] and the all-ones matrix [Formula: see text], that is [Formula: see text], where [Formula: see text] and [Formula: see text]. The cozero-divisor graph [Formula: see text] of a finite commutative ring [Formula: see text] with unity is a simple undirected graph with the set of all nonzero nonunits of [Formula: see text] as vertices and two vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text] and [Formula: see text]. In this paper, we study structural properties of [Formula: see text] by defining an equivalence relation on its vertex set in terms of principal ideals of the ring [Formula: see text]. Then we obtain the universal adjacency eigenpairs of [Formula: see text] and its complement, and as a consequence one may obtain several spectra like the adjacency, Seidel, Laplacian, signless Laplacian, normalized Laplacian, generalized adjacency and convex linear combination of the adjacency and degree diagonal matrix of [Formula: see text] and [Formula: see text] in an unified way. Moreover, we get the universal adjacency eigenpairs of the cozero-divisor graph and its complement for a reduced ring and the ring of integers modulo [Formula: see text] in a simpler form.
{"title":"Universal adjacency spectrum of the cozero-divisor graph and its complement on a finite commutative ring with unity","authors":"Saraswati Bajaj, P. Panigrahi","doi":"10.1142/s1793830923501203","DOIUrl":"https://doi.org/10.1142/s1793830923501203","url":null,"abstract":"For a finite simple undirected graph [Formula: see text], the universal adjacency matrix [Formula: see text] is a linear combination of the adjacency matrix [Formula: see text], the degree diagonal matrix [Formula: see text], the identity matrix [Formula: see text] and the all-ones matrix [Formula: see text], that is [Formula: see text], where [Formula: see text] and [Formula: see text]. The cozero-divisor graph [Formula: see text] of a finite commutative ring [Formula: see text] with unity is a simple undirected graph with the set of all nonzero nonunits of [Formula: see text] as vertices and two vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text] and [Formula: see text]. In this paper, we study structural properties of [Formula: see text] by defining an equivalence relation on its vertex set in terms of principal ideals of the ring [Formula: see text]. Then we obtain the universal adjacency eigenpairs of [Formula: see text] and its complement, and as a consequence one may obtain several spectra like the adjacency, Seidel, Laplacian, signless Laplacian, normalized Laplacian, generalized adjacency and convex linear combination of the adjacency and degree diagonal matrix of [Formula: see text] and [Formula: see text] in an unified way. Moreover, we get the universal adjacency eigenpairs of the cozero-divisor graph and its complement for a reduced ring and the ring of integers modulo [Formula: see text] in a simpler form.","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140510699","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 : 2024-01-05DOI: 10.1142/s1793830924500022
H. M. A. Siddiqui, Khadija Mazhar, Muhammad Kamran Siddiqui, Muhammad Faisal Nadeem
{"title":"On Fault-Tolerant Metric Dimension of Supramolecular Networks","authors":"H. M. A. Siddiqui, Khadija Mazhar, Muhammad Kamran Siddiqui, Muhammad Faisal Nadeem","doi":"10.1142/s1793830924500022","DOIUrl":"https://doi.org/10.1142/s1793830924500022","url":null,"abstract":"","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139450241","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 : 2023-12-14DOI: 10.1142/s179383092350115x
Tahir Shamsher, S. Pirzada
{"title":"Eigenvalues of the generalized subdivision graph with applications to graph energy","authors":"Tahir Shamsher, S. Pirzada","doi":"10.1142/s179383092350115x","DOIUrl":"https://doi.org/10.1142/s179383092350115x","url":null,"abstract":"","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139180212","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 : 2023-12-14DOI: 10.1142/s1793830923501124
Pranava K. Jha
{"title":"A hierarchical structure of the quad-cube and the associated diameter, domination, and Hamiltonicity","authors":"Pranava K. Jha","doi":"10.1142/s1793830923501124","DOIUrl":"https://doi.org/10.1142/s1793830923501124","url":null,"abstract":"","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139179324","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 : 2023-12-14DOI: 10.1142/s1793830923501185
J. Sivakumar, A. Wilson Baskar, R. Sundareswaran, V. Swaminathan
{"title":"Weakly connected resolving sets in graphs","authors":"J. Sivakumar, A. Wilson Baskar, R. Sundareswaran, V. Swaminathan","doi":"10.1142/s1793830923501185","DOIUrl":"https://doi.org/10.1142/s1793830923501185","url":null,"abstract":"","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139179081","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 : 2023-12-14DOI: 10.1142/s1793830923501148
Lisbeth D. Delgado-Ordonez, John H. Castillo, Alexander Holguín-Villa
{"title":"On the hasse diagram of binary linear codes","authors":"Lisbeth D. Delgado-Ordonez, John H. Castillo, Alexander Holguín-Villa","doi":"10.1142/s1793830923501148","DOIUrl":"https://doi.org/10.1142/s1793830923501148","url":null,"abstract":"","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139179747","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 : 2023-12-14DOI: 10.1142/s1793830923501173
Xianxi Wu, Danjun Huang
{"title":"Equitable coloring of planar graphs without 5-cycles and chordal 4-cycles","authors":"Xianxi Wu, Danjun Huang","doi":"10.1142/s1793830923501173","DOIUrl":"https://doi.org/10.1142/s1793830923501173","url":null,"abstract":"","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139180012","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 : 2023-12-14DOI: 10.1142/s1793830923501161
A. Santhakumaran, M. Mahendran, K. Ganesamoorthy
{"title":"On the open monophonic number of a graph","authors":"A. Santhakumaran, M. Mahendran, K. Ganesamoorthy","doi":"10.1142/s1793830923501161","DOIUrl":"https://doi.org/10.1142/s1793830923501161","url":null,"abstract":"","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139180167","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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