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 |
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Pages (from-to) | 131-135 |
Number of pages | 5 |
Journal | Graphs and Combinatorics |
Volume | 19 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2003 |