Integral complete multipartite graphs Original Research Article

A graph is called integral if all eigenvalues of its adjacency matrix are integers. In this paper, we investigate integral complete r-partite graphs image with image. We can construct infinite many new classes of such integral graphs by solving some certain Diophantine equations. These results are different from those in the existing literature. For image, we give a positive answer to a question of Wang et al. [Integral complete r-partite graphs, Discrete Math. 283 (2004) 231–241]. The problem of the existence of integral complete multipartite graphs image with arbitrarily large number s remains open.