Annihilator graphs derived from group rings

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P K Prasobha
G Suresh Singh


Let RG be the group ring of the group G over a ring R and let Z(RG) be the collection of all non-zero zero divisors in a finite group ring RG. And, for x ∈ Z(RG), ann(x) = { rRG | rx = 0}. The annihilator graph of RG denoted as AG(RG), and is defined as the graph whose vertex set is the elements of non-zero zero divisors in RG and two distinct vertices vx and vy are adjacent if and only if ann(x) ∩ ann(y) ≠ 0. In this paper we try to characterize the properties of annihilator graphs in group rings.


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Prasobha, P. K., & Singh, G. S. (2023). Annihilator graphs derived from group rings. Gulf Journal of Mathematics, 15(2), 109-116.