On the dominant local metric dimension of some planar graphs

Abstract

Dominant local metric dimension (DLMD) combines two interesting graph theory concepts: domination and local metric dimension (LMD). Graph invariants are a fantastic tool for analyzing graph abstract structures. Metric dimension and DLMD as graph invariants have a wide range of applications, which includes robot navigation, pharmaceutical chemistry, pattern recognition, and image processing. In this paper, we computed the DLMD of the prism graph [Formula: see text], antiprism graph [Formula: see text], and the sunflower graph [Formula: see text].