Abstract
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.
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