# Maximal energy bipartite graphs

Koolen, J. and Moulton, V. ORCID: https://orcid.org/0000-0001-9371-6435 (2003) Maximal energy bipartite graphs. Graphs and Combinatorics, 19 (1). pp. 131-135. ISSN 0911-0119

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## Abstract

Given a graph $G$, its energy $E(G)$ is defined to be the sum of the absolute values of the eigenvalues of $G$. This quantity is used in chemistry to approximate the total $\pi$-electron energy of molecules and in particular, in case $G$ is bipartite, alternant hydrocarbons. Here we show that if $G$ is a bipartite graph with $n$ vertices, then $E(G) \leq \frac{n}{\sqrt{8}}(\sqrt{2} + \sqrt{n})$ must hold, characterize those bipartite graphs for which this bound is sharp, and provide an infinite family of maximal energy bipartite graphs.

Item Type: Article Faculty of Science > School of Computing Sciences http://dx.doi.org/10.1007/s00373-002-048... Vishal Gautam 13 Jun 2011 11:54 24 Oct 2022 02:58 https://ueaeprints.uea.ac.uk/id/eprint/22439 10.1007/s00373-002-0487-7