On spectral radius and energy of complete multipartite graphs

Abstract

Let Kn1;n2...;np denote the complete p-partite graph, p > 1, on n = n1+n2+...+np vertices and let n1≥ n2 ≥ ...≥ np > 0. We show that for a fixed value of n, both the spectral radius and the energy of complete p-partite graphs are minimal for complete split graph CS(n; p - 1) and are maximal for Tuŕan graph T(n; p).