SOME PROPERTIES OF FINITE {0,1}-GRAPHS

Abstract

Let G=(V ,E) be a connected graph , X be a subset of V , Abe a finite subset of non-negative integers and n (x, y) be the total numberof neighbours of any two vertices x, y of X. The set X is called A-semisetif n (x, y) ∈ A for any two vertices x ande y of X.If X is a A-semiset,but not B-semiset for any subset B of A ,the set X is called A-set.Thegraph G=(V ,E) is a A-semigraph and A-graph if V is the A-semiset and Aset, respectively. Mulder [2] observed that {0, λ}-semigraphs(these graphs arecalled (0, λ)-graphs by Mulder [2]), (λ ≥ 2) , are regular. Furthermore a lowerbound for the degree of {0, λ}-semigraphs with diameter at least four wasderived by Mulder [2].In this paper, we determined basic properties of finite bigraphs with atleast one {0,1}-part