On the Total Graph of a Finite Commutative Ring
Let $R$ be a finite commutative ring with $1\ne 0$. In this article, we study the total graph of $R$, denoted by $τ(R)$, determine some of its basic graph-theoretical properties, determine when it is Eulerian, and find some conditions under which this graph is isomorphic to $Cay(R,Z(R)\backslash\lbrace 0\rbrace)$. We shall also compute the domination number of $τ(R).
math.AC↗