STRONG VERTEX COLOURING OF CARTESIAN PRODUCT OF GRAPHS

Abstract

For  Graph G[V,E],  strong vertex colouring is the proper colouring of vertices c : V → {1,2,3,...,x} such that for every vertex u ∈ V (G), all neighbours of u receive pairwise distinct colours; that is, if v, w ∈ N(u) then c(v)  c(w). Furthermore, all super neighbours of u (vertices at distance two from u) may receive the same colour. The smallest value of k for which this type of colouring occurs is named as strong vertex colouring number, represented as svc(G). This paper, throws light on the strong vertex colouring of the wheel graph, the star graph, and Cartesian products of graphs involving paths and cycles. These findings advances understanding of graph product structures and provide practical applications to resource distribution in network systems.