Maximal energy bipartite graphs

Jack H. Koolen, Vincent Moulton

Research output: Contribution to journalArticlepeer-review

95 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)131-135
Number of pages5
JournalGraphs and Combinatorics
Issue number1
Publication statusPublished - 2003

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