The energy of random graphs |
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Authors: | Wenxue Du Yiyang Li |
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Institution: | Center for Combinatorics and LPMC-TJKLC, Nankai University, Tianjin 300071, PR China |
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Abstract: | In 1970s, Gutman introduced the concept of the energy E(G) for a simple graph G, which is defined as the sum of the absolute values of the eigenvalues of G. This graph invariant has attracted much attention, and many lower and upper bounds have been established for some classes of graphs among which bipartite graphs are of particular interest. But there are only a few graphs attaining the equalities of those bounds. We however obtain an exact estimate of the energy for almost all graphs by Wigner’s semi-circle law, which generalizes a result of Nikiforov. We further investigate the energy of random multipartite graphs by considering a generalization of Wigner matrix, and obtain some estimates of the energy for random multipartite graphs. |
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Keywords: | 15A52 15A18 05C80 05C90 92E10 |
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