Abstract

•  is a complete graph with vertices. ( )  is a graph containing  copies of with each vertex of a is only adjacent to a vertex of each of the other . We will show that the adjacency matrix of ( )  has (i) ( – 1)( – 1) eigenvalues of –2 (ii)  – 1 eigenvalues of – 2 (iii) – 1 eigenvalues of  – 2 (iv) an eigenvalue of +  – 2.