Publication Type : Journal Article
Publisher : Springer
Source : The Journal of Analysis
Url : https://link.springer.com/article/10.1007/s41478-018-0094-5
Campus : Nagercoil
School : School of Computing
Year : 2019
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=Γ(R,U(R),U(R)) 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. In this paper, we give a necessary and sufficient condition for Γ to be unicyclic or split or claw-free. Also, we give a necessary and sufficient condition for Γ to be claw-free or unicyclic or pancyclic.
Cite this Research Publication : Thirugnanam, T. C,Anukumar Kathirvel Selvaraj, Note on generalized Cayley graph of finite rings and its complement, The Journal of Analysis, 27, 555-566, 2019.