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Proof of a conjecture on the Seidel energy of graphs

Akbari, S ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1016/j.ejc.2019.103078
  3. Publisher: Academic Press , 2020
  4. Abstract:
  5. Let G be a graph with the vertex set {v1,…,vn}. The Seidel matrix of G is an [Formula presented] 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 [Formula presented], 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 [Formula presented] and, up to Seidel equivalence, the equality holds for Kn. Recently, this conjecture was proved for [Formula presented]. We establish the validity of Haemers’ Conjecture in general. © 2020 Elsevier Ltd
  6. Keywords:
  8. Source: European Journal of Combinatorics ; Volume 86 , 2020
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0195669819301799