The local complement metric dimension of graphs

Abstract

The metric dimension of graphs has been extended in some types and variations such as local metric dimension and complement metric dimension of graphs. Merging two concepts is one way of developing the concept of graph theory as a branch of mathematics. These two variations motivated us to construct a new concept of metric dimension so called local complement metric dimension. We apply this new concept to some particular classes of graphs and the corona product of two graphs. We also characterize the local complement metric dimension of graphs with certain properties, namely, bipartite graphs and odd cycle graphs. Furthermore, we discover the local complement metric dimension of the corona product of two particular graphs as well as the corona product of two general graphs.