On Integral Graphs Which Belong to the Class

Abstract.

Let G be a simple graph and let ¯G denote its complement. A graph G is said to be integral if its spectrum contains integral values. If is integral with α>1 and a>b, where mG denotes the m-fold union of the graph G, we show that it belongs to the class of integral graphs where (i) (kn ² s ²+km nst+ms,km ² t ²+kmnst+ms)=τ such that (m,τ)=1 and (s,τ)=1; (ii) k,m,n,s,t,z∈ℕ such that (k,m)=1, (k,s)=1, (m,n)=1, (m,s)=1, (n,t)=1 and (s,t)=1; and (iii) ns>m t.