Some properties of graphs constructed from 2-designs

Let D=(P,B)D=(P,B) be any nontrivial nonsymmetric 2-(v, k, λ  ) design. In this paper we construct a connected, regular and bipartite graph, say IGv,b(D),IGv,b(D), from DD. Some graphic properties of IGv,b(D)IGv,b(D) are investigated. In particular, the results in the paper bridges the equivalency between edge-transitivity of IGv,b(D)IGv,b(D) and flag-transitivity of DD. With the equivalency, it is obtained that IGv,b(D)IGv,b(D) is a semisymmetric graph as long as DD is a nonsymmetric flag-transitive 2-(v, k, λ) design.