Publication Type : Journal Article
Publisher : Springer
Source : Indian Journal of Pure and Applied Mathematics
Url : https://link.springer.com/article/10.1007/s13226-020-0415-7
Campus : Nagercoil
School : School of Computing
Year : 2020
Abstract : Let R be a finite commutative ring with nonzero identity and U(R) be the set of all units of R. The graph Γ is the simple undirected graph with vertex set R in which two distinct vertices x and y are adjacent if and only if there exists a unit element u in U(R) such that x + uy is a unit in R. Also, Γ¯ denotes the complement of Γ. In this paper, we find the domination number γ of Γ as well as Γ¯ and characterize all γ-sets in Γ and Γ¯. Also, we obtain the bondage number of Γ. Further, we obtain the values of some domination parameters like independent, strong and weak domination numbers of Γ¯.
Cite this Research Publication : Tamizh Chelvam, T., Anukumar Kathirvel, S.,Balamurugan M., Domination in generalized unit and unitary Cayley graphs of finite rings, Indian Journal of Pure and Applied Mathematics, 51(2), 533-556, 2020.