M-Complementary Distance Uniform Matrix of a Graph

A graph G = (V,E) is Complementary Distance Pattern Uniform if there exists M ⊂ V (G) such that fM (u) = {d(u, v) : v ∈ M}, for every u ∈ V (G)−M , is independent of the choice of u ∈ V (G)−M and the set M is called the Complementary Distance Pattern Uniform Set (CDPU set). The M -Complementary Distance Uniform Matrix (M CDU Matrix), CM (G) = [cij ] of G of order n is a p × m matrix, where m is the cardinality of the CDPU set M and p = |V (G) − M |, having entries cij = d(vi, vj) where vi ∈ V (G) and vj ∈ M . In this paper, we initiate a study on M -CDU Matrix of a graph and a k-colorable CDPU graph. Mathematics Subject Classification: 05C22