Bi-Distance Pattern Uniform Number

A graph G = (V,E) is BiDistance Pattern Uniform if there exists M ⊆ V (G) such that the M−distance pattern fM(u) = {d(u, v) : v ∈ M} is identical for all u in M and fM (v) is identical for all v in V −M. The set M is called Bi-DPU set. The least cardinality of Bi-DPU set in G is called the Bi-DPU number of G. In this paper, we initiate a study on Bi-DPU number of different classes of graphs. Mathematics Subject Classification: 05C78