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Journal of Mathematical Chemistry

, Volume 43, Issue 2, pp 713–718 | Cite as

Sharp upper bounds for total π-electron energy of alternant hydrocarbons

  • Ji-Ming Guo
Article
The energy E(G) of a graph G is defined as the sum of the absolute values of all the eigenvalues of the adjacency matrix of the graph G. This quantity is used in chemistry to approximate the total π-electron energy of molecules and in particular, in case G is bipartite, alternant hydrocarbons. In this paper, we show that if G = (V 1, V 2; E) is a bipartite graph with \(m\geqslant n_1\) edges and \(|V_1|=n_1\geqslant n_2=|V_2|\), then
$$ E(G)\leqslant \frac{2m}{\sqrt{n_1n_2}}+2\sqrt{(n_2-1) \left(m-\frac{m^2}{n_1n_2}\right)} $$
and
$$ E(G)\leqslant \sqrt{n_1n_2}(1+\sqrt{n_2}) $$
must hold.

Keywords

alternant hydrocarbons energy upper bound 

AMS Subject Classification

05C50 05C35 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Applied MathematicsChina University of PetroleumShandongPeople’s Republic of China

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