Domination number of total graph of module

 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 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})).

کلیدواژه ها:

total graph ، domination number ، Module