Metric Dimension of Honeycomb Rectangular Torus

Abstract

Distance between two vertices of a graph is number of edges in a shortest path between them. One vertex having different distance from two distinct vertices is said to be a resolved vertex. Resolving set is a subset of vertex set of a graph and it consists of such vertices which resolve all the vertices of a graph. Metric dimension is an integer that is associated to resolving set and its defined as minimum count of resolving set. Honeycomb rectangular torus is one of the type of honeycomb torus. In this thesis, we will discuss metric dimension of honeycomb rectangular Torus. Metric dimension of honeycomb rectangular torus ( , ) for case (2, ) is 3. Metric dimension of honeycomb rectangular torus ( , ) > 4 for = 4 and is any even integer.