VERTEX COLOURING OF FINITE NETWORKS WITH RESPECT TO AVERAGE DISTANCE

For a finite network, represented as a graph G = (V, E) with average distance μ(G), the average distance colouring of G is a function c from V to the set of non-negative integers, such that for any v ∈ V , |c(v) − c(u)| ≥ 1 for all u ∈ V such that d(u, v) ≤ ⌈μ⌉. In this paper, we find the average distance colouring number of some special types of networks and present a greedy algorithm to colour any graph with average distance colouring constraint.