Resolvability in complement of the intersection graph of annihilator submodules of a module

	Resolvability in complement of the intersection graph of annihilator submodules of a module
Journal of Algebra and Related Topics
دوره 8، شماره 1، شهریور 2020، صفحه 27-37 اصل مقاله (295.18 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22124/jart.2020.15786.1192
نویسندگان
Sh. Payrovi^* ؛ S. B. Pejman؛ S. Babaei
Department of Mathematics, Imam Khomeini International University, Qazvin, Iran
چکیده
Let $R$ be a commutative ring and $M$ be an $R$-module. The intersection graph of annihilator submodules of $M$, denoted by ${GA(M)}$, is a simple undirected graph whose vertices are the classes of elements of $Z(M)\setminus {\rm Ann}_R(M)$ and two distinct classes $[a]$ and $[b]$ are adjacent if and only if ${\rm Ann}_M(a)\cap {\rm Ann}_M(b)\not=0$. In this paper, we study the diameter and girth of $\overline{GA(M)}$. Furthermore, we calculate the domination number, metric dimension, adjacency metric dimension and local metric dimension of $\overline{GA(M)}$.
کلیدواژه‌ها
Prime submodule‎؛ ‎Annihilator submodule‎؛ ‎Intersection graph

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