Discrete Mathematics, Algorithms and Applications, Volume (7), No (1), Year (2014-2) , Pages (145006801-145006811)
Title : ( A generalization of commuting graphs )
Authors: Mojgan Afkhami , Zahra Barati , Seyede Nesa Hoseini , Kazem Khashyarmanesh ,Access to full-text not allowed by authors
Abstract
Let R be a ring with the identity element 1, α be an endomorphism of R and b be a left α-derivation. In this paper, we introduce a generalization of a commuting graph, which is denoted by ΓR(α, b), as a directed graph with vertex set R and, for two distinct vertices x and y, there is an arc from x to y if and only if xy = α(y)x + b(y). We study some basic properties of ΓR(α, b). Also, we investigate the planarity and genus of the graph ΓR(α, 0).