Metric Dimension of Corona Product and Join Graph of Zero Divisor Graphs of Direct Product of Finite Fields

The metric dimension of a graph is the smallest number of vertices such that all vertices are uniquely determined by their distances to the chosen vertices. The corona product of graphs G and H is the graph G ⊙ H obtained by taking one copy of G, called the center graph, | V (G) | copies of H, called the outer graph, and making the j t h vertex of G adjacent to every vertex of the j t h copy of H, where 1 ⩽ j ⩽ | V (G) |. The Join graph G + H of two graphs G and H is the graph with vertex set V (G + H) = V (G) ∪ V (H) and edge set E (G + H) = E (G) ∪ E (H) ∪ u v: u ∈ V (G), v ∈ V (H). In this paper, we determine the Metric dimension of Corona product and Join graph of zero divisor graphs of direct product of finite fields.