On Examining Metric Dimension Through Edge Contraction in Certain Families of Graphs

In graph theory, the Metric Dimension (MD) is an elementary metric that affords evidence nearly the essential selves of graphs. We reconnoiter the MD in the venue of edge-contracted regular graphs in this paper, with exceptional devotion to the Antiprism, Petersen, and Harary graphs. Our effort creates a vital bond between antiprism and its edge-contracted counterpart: we give a scheme to regulate the MD of the edge-contracted graph, given the MD of the novel graph. We likewise inspect how edge contraction affects regular graphs’ MDs, providing insight into how this operation deviations both the MD and the underlying graph topology. By providing supportive means for the exploration and alteration of regular graphs in a variety of real-world circumstances, our investigation elucidates these belongings and improves the field of graph theory.