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 \( G \odot H \) obtained by taking one copy of \( G \), called the center graph, \( |V(G)| \) copies of \( H \), called the outer graph, and making the \( j^{th} \) vertex of \( G \) adjacent to every vertex of the \( j^{th} \) copy of \( H \), where \( 1 \leqslant j \leqslant |V(G)| \). The Join graph \( G + H \) of two graphs \( G \) and \( H \) is the graph with vertex set \( V(G + H)=V(G) \cup V(H) \) and edge set \( E(G + H)=E(G) \cup E(H) \cup \{uv :u \in V(G),v \in V(H)\} \). In this paper, we determine the Metric dimension of Corona product and Join graph of zero divisor graphs of direct product of finite fields.