On spectral radius and energy of complete multipartite graphs

Abstract

Let K_{n1, n2, …, np} denote the complete p-partite graph, p > 1, on n = n₁ + n₂ + ⋯ + n_p vertices and let n₁ ≥ n₂ ≥ ⋯ ≥ n_p > 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 Turán graph T(n, p).