@article { author = {Shariatnia, Abbas and Tehranian, Abolfazl}, title = {Domination number of total graph of module}, journal = {Algebraic Structures and Their Applications}, volume = {2}, number = {1}, pages = {1-9}, year = {2015}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {}, 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 investigate the necessary conditions for being $\mathbb{Z}_{n}$ as module over $\mathbb{Z}_{m}$ and we find the domination number of $T(\Gamma(\mathbb{Z}_{n}))$.}, keywords = {total graph,domination number,Module}, url = {https://as.yazd.ac.ir/article_665.html}, eprint = {https://as.yazd.ac.ir/article_665_fa2f8c151be2c96db3d6e8ef1e2c192f.pdf} }