On the maximum spectral radius of multipartite graphs

Abstract

Let be an integer. A graph is called r – partite if V admits a partition into r parts such that every edge has its ends in different parts. All of the r – partite graphs with given integer r consist of the class of multipartite graphs. Let be the set of multipartite graphs with r vertex parts, n nodes and diameter D. In this paper, we characterize the graphs with the maximum spectral radius in Furthermore, we show that the maximum spectral radius is not only a decreasing function on D, but also an increasing function on r.