On the local metric dimension of generalized wheel graph

Abstract

Metric dimension and local metric dimension are distance-based tools that find their applications in robot navigation, combinatorial optimization, pattern recognition, image processing, integer programming, and many more. A study based on the selection of the minimum number of vertices in a graph that will separate all the neighboring vertices in terms of distance between the vertices is given by the local metric basis problem. It is well known that the problem of finding the local metric basis of a graph is NP-complete. In this paper, the local metric dimension of double wheel graph [Formula: see text], generalized wheel graph [Formula: see text], and closed helm graph [Formula: see text] had been computed. It has been found that these graphs have unbounded local metric dimensions.