Publication Type : Journal Article
Source : Journal of Algebra and Its Applications
Url : https://www.worldscientific.com/doi/abs/10.1142/S0219498819500063
Campus : Nagercoil
School : School of Computing
Year : 2019
Abstract : Let RR be a finite commutative ring with nonzero identity and U(R)U(R) be the set of all units of R.R. The graph ΓΓ is the simple undirected graph with vertex set RR in which two distinct vertices xx and yy are adjacent if and only if there exists a unit element uu in U(R)U(R) such that x+uyx+uy is a unit in R.R. In this paper, we obtain degree of all vertices in ΓΓ and in turn provide a necessary and sufficient condition for ΓΓ to be Eulerian. Also, we give a necessary and sufficient condition for the complement ΓΓ to be Eulerian, Hamiltonian and planar.
Cite this Research Publication : Tamizh Chelvam T., & Anukumar Kathirvel S., Generalized unit and unitary Cayley graphs of finite rings, Journal of Algebra and Its Applications, 18(01), 1950006, 2019.