2009/08/19 by Ebrahim Ghorbani, Ghorbani, Ebrahim, Jack H. Koolen +3
Computer Science · Mathematics · #05C50 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.0908.2667
openalex publication_date 2009/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a graph on n vertices with r := \lfloor n/2 \rfloor and let λ1 ≥...≥ λn be adjacency eigenvalues of G. Then the Hückel energy of G, HE(G), is defined as \he(G) = ll 2∑i=1r λi, amp; \hboxif n= 2r; 2∑i=1r λi + λr+1, amp; \hboxif n= 2r+1. 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, λ, 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.