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Bounds for the Huckel energy of a graph

Ghorbani, E ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: https://doi.org/10.37236/223
  3. Publisher: 2009
  4. Abstract:
  5. Let G be a graph on n vertices with r := [n/2] and let γ 1 ≥ · · · ≥ γ n be adjacency eigenvalues of G. Then the Ḧuckel energy of G, HE(G), is defined as [Equation presented] The concept of Hückel energy was introduced by Coulson as it gives a good approximation for the π-electron energy of molecular graphs. We obtain two upper bounds and a lower bound for HE(G). When n is even, it is shown that equality holds in both upper bounds if and only if G is a strongly regular graph with parameters (n, k, γ, μ) = (4t2 + 4t + 2, 2t2 + 3t + 1, t2 + 2t, t2 + 2t + 1), for positive integer t. Furthermore, we will give an infinite family of these strongly regular graph whose construction was communicated by Willem Haemers to us. He attributes the construction to J.J. Seidel
  6. Keywords:
  7. Combinatorics
  8. Source: Electronic Journal of Combinatorics ; Volume 16, Issue 1 R , 2009 ; 10778926 (ISSN)
  9. URL: https://www.combinatorics.org/ojs/index.php/eljc/article/view/v16i1r134