# Maximal energy bipartite graphs

J. Koolen, V. Moulton

Research output: Contribution to journalArticlepeer-review

87 Citations (Scopus)

## 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.
Original language English 131-135 5 Graphs and Combinatorics 19 1 https://doi.org/10.1007/s00373-002-0487-7 Published - 2003