Proof of a Conjecture on the Seidel Energy of Graphs

2019/01/20 by Akbari, Saieed, Einollahzadeh, Mostafa, Karkhaneei, Mohammad Mahdi +1 · 1 citation
#05C50 #15A18 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.06692

Abstract

Let G be a graph with the vertex set \lbrace v₁,…,v_n \rbrace. The Seidel matrix of G is an n× n matrix whose diagonal entries are zero, ij-th entry is -1 if v_i and v_j are adjacent and otherwise is 1 . The Seidel energy of 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 K_n . We establish the validity of Haemers' Conjecture in general.

Cited by

• A graph energy conjecture through the lenses of semidefinite programming

Related

• On eigenvalues of Seidel matrices and Haemers' conjecture
• An improved lower bound for the Seidel energy of tree graphs
• On the spectrum and energy of Seidel matrix for chain graphs
• On the eigenvalues of some signed graphs
• On the Sombor characteristic polynomial and Sombor energy of a graph