A set $H subseteq V(G)$ is eccentric hub set of a graph $G$ if $H$ is a hub set of $G$ and also every $v in V(G) backslash H$ has an eccentric vertex in $H$. The minimal eccentric hub set with minimum cardinality is called minimum eccentric hub set. Its cardinality is eccentric hub number of $G$, denoted by $e h(G)$. In this paper, we deduce some results and bounds on this parameter. Further, we have studied about total number of minimum eccentric hub sets and eccentric hub graphs. Received: June 14, 2023; Accepted: August 2, 2023
集合H subseteq V(G)$是图$G$的偏心轮毂集，如果$H$是$G$的轮毂集并且V(G) 反斜杠H$中的每个$ V 在$H$中都有一个偏心顶点。具有最小基数的最小偏心轮毂集称为最小偏心轮毂集。其基数为$G$的偏心轮毂数，记为$e h(G)$。在本文中，我们推导了关于该参数的一些结果和界。进一步研究了最小偏心轮毂集的总数和偏心轮毂图。收稿日期:2023年6月14日;录用日期:2023年8月2日
{"title":"THE ECCENTRIC HUB NUMBER OF A GRAPH","authors":"Veena Mathad","doi":"10.17654/0974165823062","DOIUrl":"https://doi.org/10.17654/0974165823062","url":null,"abstract":"A set $H subseteq V(G)$ is eccentric hub set of a graph $G$ if $H$ is a hub set of $G$ and also every $v in V(G) backslash H$ has an eccentric vertex in $H$. The minimal eccentric hub set with minimum cardinality is called minimum eccentric hub set. Its cardinality is eccentric hub number of $G$, denoted by $e h(G)$. In this paper, we deduce some results and bounds on this parameter. Further, we have studied about total number of minimum eccentric hub sets and eccentric hub graphs. Received: June 14, 2023; Accepted: August 2, 2023","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135435024","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}
Sonny C. Abdurasid, Bayah J. Amiruddin, Jeffrey Imer C. Salim, Rosalio G. Artes, Jr.
{"title":"CONVEX NEIGHBORHOOD POLYNOMIAL OF GRAPHS","authors":"Sonny C. Abdurasid, Bayah J. Amiruddin, Jeffrey Imer C. Salim, Rosalio G. Artes, Jr.","doi":"10.17654/0974165823061","DOIUrl":"https://doi.org/10.17654/0974165823061","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43378201","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}
{"title":"k-PRIME TOTAL LABELING OF SHELL RELATED GRAPHS","authors":"S. T. Arockiamary","doi":"10.17654/0974165823033","DOIUrl":"https://doi.org/10.17654/0974165823033","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45969775","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}
{"title":"ON CORONA PRODUCT OF ZERO-DIVISOR GRAPHS OF DIRECT PRODUCT OF FINITE FIELDS","authors":"Subhash Mallinath Gaded, N. Narayana","doi":"10.17654/0974165823060","DOIUrl":"https://doi.org/10.17654/0974165823060","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44674624","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}
A graph $G$ is co-segregated if $text{deg}_G(x)=text{deg}_G(y),$ then $xy in E(G)$. The co-segregated polynomial of a graph $G$ of order $n$ is given by $CoS(G,x)=sum_{k=1}^{n}C(k)x^k$, where $C(k)$ is the number of co-segregated subgraphs of $G$ of order $k$. We characterize a co-segregated subgraph of a graph and also of a graph under some binary operations. Using these characterizations, we obtain co-segregated polynomials of such graphs.
{"title":"CO-SEGREGATED POLYNOMIAL OF GRAPHS","authors":"Aziz B. Tapeing, Ladznar S. Laja","doi":"10.17654/0974165823059","DOIUrl":"https://doi.org/10.17654/0974165823059","url":null,"abstract":"A graph $G$ is co-segregated if $text{deg}_G(x)=text{deg}_G(y),$ then $xy in E(G)$. The co-segregated polynomial of a graph $G$ of order $n$ is given by $CoS(G,x)=sum_{k=1}^{n}C(k)x^k$, where $C(k)$ is the number of co-segregated subgraphs of $G$ of order $k$. We characterize a co-segregated subgraph of a graph and also of a graph under some binary operations. Using these characterizations, we obtain co-segregated polynomials of such graphs.","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49613765","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}
{"title":"RESULTS ON GRUNDY CHROMATIC NUMBER OF JOIN GRAPH OF GRAPHS","authors":"R. S. Maragatham, A. Subramanian","doi":"10.17654/0974165823058","DOIUrl":"https://doi.org/10.17654/0974165823058","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44379053","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}
D. Gibaja-Romero, J. Martínez-Flores, Diana Sánchez-Partida
{"title":"NON-COOPERATIVE BEHAVIOR IN INTERACTION OF DISTRIBUTION CENTERS","authors":"D. Gibaja-Romero, J. Martínez-Flores, Diana Sánchez-Partida","doi":"10.17654/0974165823057","DOIUrl":"https://doi.org/10.17654/0974165823057","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42462863","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}
ArunMarry Ann E. Anore, Jocecar L. Hinampas, Renario G. Hinampas
{"title":"1-MOVABLE DOUBLE OUTER-INDEPENDENT DOMINATION IN GRAPHS","authors":"ArunMarry Ann E. Anore, Jocecar L. Hinampas, Renario G. Hinampas","doi":"10.17654/0974165823056","DOIUrl":"https://doi.org/10.17654/0974165823056","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42311871","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}
Amelia L. Arriesgado, Jeffrey Imer C. Salim, Rosalio G. Artes, Jr.
{"title":"POLYNOMIAL REPRESENTATION OF THE NEIGHBORHOOD SYSTEMS OF CLIQUES IN THE CORONA OF GRAPHS","authors":"Amelia L. Arriesgado, Jeffrey Imer C. Salim, Rosalio G. Artes, Jr.","doi":"10.17654/0974165823054","DOIUrl":"https://doi.org/10.17654/0974165823054","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41789573","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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