On spectral radius and energy of complete multipartite graphs - Stevanović, Dragan (Ars mathematica contemporanea, 2015)
Let ?$K_{n_1, n_2, … , n_p}$? denote the complete ?$p$?-partite graph, ?$p > 1$?, on ?$ n = n_1 + n_2 + … + n_p$? vertices and let ?$n_1 \ge n_2 \ge … \ge 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)$?.
Keywords: complete multipartite graph; complete split graph; energija grafa; graph energy; polni razcepljeni graf; polni večdelni graf; spectral radius of graph; spektralni radij grafa; Turan graph; Turánov graf