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Patwari, D., Saikia, H., Goswami, J.. (1401). Some results on domination in the generalized total graph of a commutative ring. فیزیولوژی و بیوتکنولوژی آبزیان, 10(1), 119-128. doi: 10.22124/jart.2021.19238.1265
D. Patwari; H. K. Saikia; J. Goswami. "Some results on domination in the generalized total graph of a commutative ring". فیزیولوژی و بیوتکنولوژی آبزیان, 10, 1, 1401, 119-128. doi: 10.22124/jart.2021.19238.1265
Patwari, D., Saikia, H., Goswami, J.. (1401). 'Some results on domination in the generalized total graph of a commutative ring', فیزیولوژی و بیوتکنولوژی آبزیان, 10(1), pp. 119-128. doi: 10.22124/jart.2021.19238.1265
Patwari, D., Saikia, H., Goswami, J.. Some results on domination in the generalized total graph of a commutative ring. فیزیولوژی و بیوتکنولوژی آبزیان, 1401; 10(1): 119-128. doi: 10.22124/jart.2021.19238.1265

Some results on domination in the generalized total graph of a commutative ring

Journal of Algebra and Related Topics
دوره 10، شماره 1، شهریور 2022، صفحه 119-128    اصل مقاله (255.18 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22124/jart.2021.19238.1265
نویسندگان
D. Patwari1؛ H. K. Saikia2؛ J. Goswami* 2
1Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India
2Department of Mathematics, Gauhati University, Guwahati-781014, Assam, India
چکیده
Let R be a commutative ring with nonzero identity and H be a nonempty proper subset of R such that R/H is a saturated multiplicatively closed subset of R. Anderson and Badawi [4] introduced the generalized total graph of R as an undirected simple graph GTH(R) with vertex set as R and any two distinct vertices x and y are adjacent if and only if x + y ϵ H. The main objective of this paper is to study the domination properties of the graph GTH(R). We determine the domination number of GTH(R) and its induced subgraphs GTH(H) and GTH(R/H). We establish a relationship between
the domination number of GTH(R) and the same of GTH(R/H). We also establish a relationship between diameter and domination number of GTH(R/H). In addition,we obtain the bondage number of GTH(R). Finally, a relationship between girth and bondage number of GTH(R/H) has been established.
کلیدواژه‌ها
Bondage number؛ Commutative ring؛ Domination number؛ Generalized total graph
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