Pub Date : 2022-07-04DOI: 10.1080/09728600.2022.2093145
Jishnu Sen, S. Kola
{"title":"Broadcast domination of lexicographic and modular products of graphs","authors":"Jishnu Sen, S. Kola","doi":"10.1080/09728600.2022.2093145","DOIUrl":"https://doi.org/10.1080/09728600.2022.2093145","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":"47 1","pages":"177-181"},"PeriodicalIF":1.0,"publicationDate":"2022-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90224604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-04DOI: 10.1080/09728600.2022.2094299
Yuan Chen, Guowei Dai
{"title":"Binding number and path-factor critical deleted graphs","authors":"Yuan Chen, Guowei Dai","doi":"10.1080/09728600.2022.2094299","DOIUrl":"https://doi.org/10.1080/09728600.2022.2094299","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":"52 1","pages":"197-200"},"PeriodicalIF":1.0,"publicationDate":"2022-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88264123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-30DOI: 10.1080/09728600.2022.2077674
Rajesh Singh, Purnima Gupta, S. Arumugam
{"title":"Truly non-trivial graphoidal graphs","authors":"Rajesh Singh, Purnima Gupta, S. Arumugam","doi":"10.1080/09728600.2022.2077674","DOIUrl":"https://doi.org/10.1080/09728600.2022.2077674","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":"127 1","pages":"112-117"},"PeriodicalIF":1.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73382059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-22DOI: 10.1080/09728600.2022.2088315
B. Rather, M. Aouchiche, S. Pirzada
{"title":"On the spread of the geometric-arithmetic matrix of graphs","authors":"B. Rather, M. Aouchiche, S. Pirzada","doi":"10.1080/09728600.2022.2088315","DOIUrl":"https://doi.org/10.1080/09728600.2022.2088315","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":"43 1","pages":"146-153"},"PeriodicalIF":1.0,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80234105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-16DOI: 10.1080/09728600.2023.2218917
G. Lau, J. M. Jeyaseeli, W. Shiu, S. Arumugam
We introduce a new concept in graph coloring motivated by the popular Sudoku puzzle. Let $G=(V,E)$ be a graph of order $n$ with chromatic number $chi(G)=k$ and let $Ssubseteq V.$ Let $mathscr C_0$ be a $k$-coloring of the induced subgraph $G[S].$ The coloring $mathscr C_0$ is called an extendable coloring if $mathscr C_0$ can be extended to a $k$-coloring of $G.$ We say that $mathscr C_0$ is a Sudoku coloring of $G$ if $mathscr C_0$ can be uniquely extended to a $k$-coloring of $G.$ The smallest order of such an induced subgraph $G[S]$ of $G$ which admits a Sudoku coloring is called the Sudoku number of $G$ and is denoted by $sn(G).$ In this paper we initiate a study of this parameter. We first show that this parameter is related to list coloring of graphs. In Section 2, basic properties of Sudoku coloring that are related to color dominating vertices, chromatic numbers and degree of vertices, are given. Particularly, we obtained necessary conditions for $mathscr C_0$ being uniquely extendable, and for $mathscr C_0$ being a Sudoku coloring. In Section 3, we determined the Sudoku number of various familes of graphs. Particularly, we showed that a connected graph $G$ has $sn(G)=1$ if and only if $G$ is bipartite. Consequently, every tree $T$ has $sn(T)=1$. Moreover, a graph $G$ with small chromatic number may have arbitrarily large Sudoku number. Extendable coloring and Sudoku coloring are nice tools for providing a $k$-coloring of $G$.
{"title":"Sudoku number of graphs","authors":"G. Lau, J. M. Jeyaseeli, W. Shiu, S. Arumugam","doi":"10.1080/09728600.2023.2218917","DOIUrl":"https://doi.org/10.1080/09728600.2023.2218917","url":null,"abstract":"We introduce a new concept in graph coloring motivated by the popular Sudoku puzzle. Let $G=(V,E)$ be a graph of order $n$ with chromatic number $chi(G)=k$ and let $Ssubseteq V.$ Let $mathscr C_0$ be a $k$-coloring of the induced subgraph $G[S].$ The coloring $mathscr C_0$ is called an extendable coloring if $mathscr C_0$ can be extended to a $k$-coloring of $G.$ We say that $mathscr C_0$ is a Sudoku coloring of $G$ if $mathscr C_0$ can be uniquely extended to a $k$-coloring of $G.$ The smallest order of such an induced subgraph $G[S]$ of $G$ which admits a Sudoku coloring is called the Sudoku number of $G$ and is denoted by $sn(G).$ In this paper we initiate a study of this parameter. We first show that this parameter is related to list coloring of graphs. In Section 2, basic properties of Sudoku coloring that are related to color dominating vertices, chromatic numbers and degree of vertices, are given. Particularly, we obtained necessary conditions for $mathscr C_0$ being uniquely extendable, and for $mathscr C_0$ being a Sudoku coloring. In Section 3, we determined the Sudoku number of various familes of graphs. Particularly, we showed that a connected graph $G$ has $sn(G)=1$ if and only if $G$ is bipartite. Consequently, every tree $T$ has $sn(T)=1$. Moreover, a graph $G$ with small chromatic number may have arbitrarily large Sudoku number. Extendable coloring and Sudoku coloring are nice tools for providing a $k$-coloring of $G$.","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45635141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-14DOI: 10.1080/09728600.2022.2084355
Nibedita Mandal, P. Panigrahi
{"title":"L(2, 1)-coloring and irreducible no-hole coloring of lexicographic product of graphs","authors":"Nibedita Mandal, P. Panigrahi","doi":"10.1080/09728600.2022.2084355","DOIUrl":"https://doi.org/10.1080/09728600.2022.2084355","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":"1 1","pages":"133-140"},"PeriodicalIF":1.0,"publicationDate":"2022-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74478506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-08DOI: 10.1080/09728600.2022.2084354
Seena Varghese, S. Lakshmanan, S. Arumugam
{"title":"Two extensions of Leech labeling to the class of all graphs","authors":"Seena Varghese, S. Lakshmanan, S. Arumugam","doi":"10.1080/09728600.2022.2084354","DOIUrl":"https://doi.org/10.1080/09728600.2022.2084354","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":"400 1","pages":"159-165"},"PeriodicalIF":1.0,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79806909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-06DOI: 10.1080/09728600.2022.2084356
D. Saranya, S. Jeevadoss
{"title":"Decomposition of hypercube graphs into paths and cycles of length four","authors":"D. Saranya, S. Jeevadoss","doi":"10.1080/09728600.2022.2084356","DOIUrl":"https://doi.org/10.1080/09728600.2022.2084356","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":"79 1","pages":"141-145"},"PeriodicalIF":1.0,"publicationDate":"2022-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83910104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-31DOI: 10.1080/09728600.2022.2081523
Yasmeen Akhtar
{"title":"A hyperedge coloring and application in combinatorial testing","authors":"Yasmeen Akhtar","doi":"10.1080/09728600.2022.2081523","DOIUrl":"https://doi.org/10.1080/09728600.2022.2081523","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":"25 1","pages":"125-132"},"PeriodicalIF":1.0,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82606172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-30DOI: 10.1080/09728600.2022.2077675
Afsaneh Rezaei, K. Khashyarmanesh, M. Afkhami
{"title":"On the metric dimension of Cayley graphs","authors":"Afsaneh Rezaei, K. Khashyarmanesh, M. Afkhami","doi":"10.1080/09728600.2022.2077675","DOIUrl":"https://doi.org/10.1080/09728600.2022.2077675","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":"18 1","pages":"118-124"},"PeriodicalIF":1.0,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91226264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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