The energy of random signed graph

A signed graph Gamma(G) is a graph with a sign attached to each of its edges, where G is the underlying graph of Gamma(G). The energy of a signed graph Gamma(G) is the sum of the absolute values of the eigenvalues of the adjacency matrix A(Gamma(G)) of Gamma(G). The random signed graph model G(n), (p, q) is defined as follows: Let p, q >= 0 be fixed, 0 < p + q < 1. Given a set of n vertices, between each pair of distinct vertices there is either a positive edge with probability p or a negative edge with probability q, or else there is no edge with probability 1 - (p + q). The edges between different pairs of vertices are chosen independently. In this paper, we obtain an exact estimate of energy for almost all signed graphs. Furthermore, we establish lower and upper bounds to the energy of random multipartite signed graphs. (C) 2019 Elsevier Inc. All rights reserved.