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 $\overline{GA(M)}$.
Payrovi, S. , Pejman, S. B. and Babaei, S. (2020). Resolvability in complement of the intersection graph of annihilator submodules of a module. Journal of Algebra and Related Topics, 8(1), 27-37. doi: 10.22124/jart.2020.15786.1192
MLA
Payrovi, S. , , Pejman, S. B. , and Babaei, S. . "Resolvability in complement of the intersection graph of annihilator submodules of a module", Journal of Algebra and Related Topics, 8, 1, 2020, 27-37. doi: 10.22124/jart.2020.15786.1192
HARVARD
Payrovi, S., Pejman, S. B., Babaei, S. (2020). 'Resolvability in complement of the intersection graph of annihilator submodules of a module', Journal of Algebra and Related Topics, 8(1), pp. 27-37. doi: 10.22124/jart.2020.15786.1192
CHICAGO
S. Payrovi , S. B. Pejman and S. Babaei, "Resolvability in complement of the intersection graph of annihilator submodules of a module," Journal of Algebra and Related Topics, 8 1 (2020): 27-37, doi: 10.22124/jart.2020.15786.1192
VANCOUVER
Payrovi, S., Pejman, S. B., Babaei, S. Resolvability in complement of the intersection graph of annihilator submodules of a module. Journal of Algebra and Related Topics, 2020; 8(1): 27-37. doi: 10.22124/jart.2020.15786.1192
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