On the metric dimension of HDN 3 and PHDN 3
F. Simon Raj, A. George · 2017 IEEE International Conference on Power, Control, Signals and Instrumentation Engineering (ICPCSI) · 2017
Let M = {m1, m2,..., mp} be an ordered set of vertices in a graph G(V, E). Then (d(u, m1), d(u, m2),..., d(u, mp)) is called the p-dimensional vector of distances coordinate or p-coordinate of a vertex u of G. The set M is called a resolving set if the vertices of G have distinct p-coordinate. A metric basis is a resolving set M with minimum cardinality. If M is a metric basis then it is clear that for each pair of vertices u and v in the set of vertices V of G not in M, there is a vertex m in M such that the distance between u and m is not equal to the distance between v and m. The cardinality of a metric basis of G is called metric dimension. The members of a metric basis are called landmarks. A metric dimension problem is to find a metric basis. The problem of finding metric dimension is an NP Complete for general graphs. In this paper we have derived certain new networks called Hex derived network three HDN 3 and Poly (Triangular and Rectangular) Hex derived network three PHDN 3 from Hexagonal network and found a resolving set for HDN 3, and PHDN 3 networks.