Acta Universitatis Sapientiae: Mathematica (Nov 2020)

On the metric dimension of strongly annihilating-ideal graphs of commutative rings

  • Soleymanivarniab V.,
  • Nikandish R.,
  • Tehranian A.

DOI
https://doi.org/10.2478/ausm-2020-0025
Journal volume & issue
Vol. 12, no. 2
pp. 358 – 369

Abstract

Read online

Let 𝒭 be a commutative ring with identity and 𝒜(𝒭) be the set of ideals with non-zero annihilator. The strongly annihilating-ideal graph of 𝒭 is defined as the graph SAG(𝒭) with the vertex set 𝒜 (𝒭)* = 𝒜 (𝒭) \{0} and two distinct vertices I and J are adjacent if and only if I ∩ Ann(J) ≠ (0) and J ∩ Ann(I) ≠ (0). In this paper, we study the metric dimension of SAG(𝒭) and some metric dimension formulae for strongly annihilating-ideal graphs are given.

Keywords