On the metric dimension of a total graph of non-zero annihilating ideals

Let R be a commutative ring with identity which is not an integral domain. An ideal I of a ring R is called an annihilating ideal if there exists r ∈ R − {0} such that Ir = (0). Visweswaran and H. D. Patel associated a graph with the set of all non-zero annihilating ideals of R , denoted by Ω( R ) as the graph with the vertex-set A ( R ) * , the set of all non-zero annihilating ideals of R and two distinct vertices I, J are joined if and only if I + J is also an annihilating ideal of R . In this paper, we study the metric dimension of Ω( R ) and provide metric dimension formulas for Ω( R ).

Abstract licence: CC BY-NC-ND

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