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

Document Type : Research Paper

Authors

Department of Mathematics, Imam Khomeini International University, Qazvin, Iran

Abstract

Let

R

be a commutative ring and

M

be an

R

-module. The intersection graph of annihilator
submodules of

M

, denoted by

G A (M)

, is a simple undirected graph whose vertices are the
classes of elements of

Z (M) ∖ {A n n}_{R} (M)

and two distinct classes

[a]

and

[b]

are adjacent if and only if

{A n n}_{M} (a) \cap {A n n}_{M} (b) \neq 0

. In this paper, we study
the diameter and girth of

\overset{―}{G A (M)}

. Furthermore, we calculate the domination number,
metric dimension, adjacency metric dimension and local metric dimension of

\overset{―}{G A (M)}

Keywords