Independent Complementary Distance Pattern Uniform Graphs

Ag raphG =( V, E) is called to be Smarandachely uniform k-graph for an integer k ≥ 1i f there existsM1 ,M 2, ··· ,M k ⊂ V (G) such that fMi (u )= {d(u, v ): v ∈ Mi} for ∀u ∈ V (G)−Mi is independent of the choice of u ∈ V (G)−Mi and integer i, 1 ≤ i ≤ k .E ach such set Mi, 1 ≤ i ≤ k is called a CDPU set (6, 7). Particularly, for k = 1, a Smarandachely uniform 1-graph is abbreviated to a complementary distance pattern uniform graph, i.e., CDPU graphs. This paper studies independent CDPU graphs.