Proof of a conjecture on the Seidel energy of graphs

Let G be a graph with the vertex set {v1,…,vn}. The Seidel matrix of G is an n×n matrix whose diagonal entries are zero, ij-th entry is −1 if vi and vj are adjacent and otherwise is 1. The Seidel energy of G, denoted by E(S(G)), is defined to be the sum of absolute values of all eigenvalues of the Seidel matrix of G. Haemers conjectured that the Seidel energy of any graph of order n is at least 2n−2 and , up to Seidel equivalence, the equality holds for Kn. Recently, this conjecture was proved for n≤12. We establish the validity of Haemers’ Conjecture in general.