Designs associated with maximum independent sets of a graph

Abstract

A (v, β o , μ)-design over regular graph G = (V, E) of degree d is an ordered pair D = (V, B), where |V| = v and B is the set of maximum independent sets of G called blocks such that if i, j ? V, i ? j and if i and j are not adjacent in G then there are exactly μ blocks containing i and j. In this paper, we study (v, β o , μ)-designs over the graphs K n × K n , T(n)-triangular graphs, L 2(n)-square lattice graphs, Petersen graph, Shrikhande graph, Clebsch graph and the Schlafli graph and non-existence of (v, β o , μ)-designs over the three Chang graphs T 1(8), T 2(8) and T 3(8).