Three Classes of Bipartite Integral Graphs

A graph G is called integral if all zeros of its characteristic polynomial P(G, x) are integers. In this paper, the bipartite graphs Kp, q(t), Kp(s), q(t) and Kp, q ≡ Kq, r are defined. We shall derive their characteristic polynomials from matrix theory. We also obtain their sufficient and necessary conditions for the three classes of graphs to be integral. These results generalize some results of Balinska et al. The discovery of these integral graphs is a new contribution to the search of integral graphs.

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