A study of the total graph

Author(s):

Abolfazl Tehranian , Hamid Reza Maimani

Message:
Abstract:
Let R be a commutative ring with $Z(R)$ its set of zero-divisors. In this paper, we study the total graph of $R$, denoted by $T(Gamma(R))$. It is the (undirected) graph with all elements of R as vertices, and for distinct $x, yin R$, the vertices $x$ and $y$ are adjacent if and only if $x + yinZ(R)$. We study the chromatic number and edge connectivity of this graph.
Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:6 Issue: 2, Nov 2011
Pages:
75 to 80
https://www.magiran.com/p909379