DETERMINING THE DOMINANT METRIC DIMENSION FOR VARIOUS GRAPHS
Iqbal M. Batiha, Iqbal Hamzah Jebril, Basma Mohamed · JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES · 2024
In this paper, we examine the dominating metric dimension of various graph types. A resolving set is a subset of vertices that uniquely identifies each vertex in the graph based on its distances to others, and the metric dimension is the minimum size of such a set. A dominating set ensures each vertex is adjacent to at least one vertex in the set. When a set is both resolving and dominating, it forms a dominating resolving set, and the smallest such set defines the dominating metric dimension, denoted as . We calculate the dominating metric dimension for the splitting graph of book graph, globe graph, tortoise graph, and graph.