DOMINATION NUMBER OF TOTAL GRAPH OF MODULE

Abstract

Let $R$ be a commutative ring and $M$ be an $R$-module with $T(M)$ as subset, the set of torsion elements. The total graph of the module denoted by $T(Gamma(M))$, is the (undirected) graph with all elements of $M$ as vertices, and for distinct elements $n,m in M$, the vertices $n$ and $m$ are adjacent if and only if $n+m in T(M)$. In this paper we study the domination number of $T(Gamma(M))$ and <br />investigate the necessary conditions for being $mathbb{Z}_{n}$ as module over $mathbb{Z}_{m}$ and we find the domination number of $T(Gamma(mathbb{Z}_{n}))$.