Volume 4, Issue 4, December 2019, Page: 94-98
The Matching Energy of Random Multipartite Graphs
Caibing Chang, School of Mathematics and Statistics, Qinghai Normal University, Xining, China
Bo Deng, School of Mathematics and Statistics, Qinghai Normal University, Xining, China; Key Laboratory of Tibetan Information Processing and Machine Translation, Xining, China; College of Science, Guangdong University of Petrochemical Technology, Maoming, China
Haizhen Ren, School of Mathematics and Statistics, Qinghai Normal University, Xining, China
Feng Fu, School of Mathematics and Statistics, Qinghai Normal University, Xining, China
Received: Sep. 22, 2019;       Accepted: Dec. 2, 2019;       Published: Dec. 7, 2019
DOI: 10.11648/j.ajmcm.20190404.12      View  297      Downloads  103
Abstract
Let Gn be a simple graph with n vertices. Gutman and Wagner founded the theory of random graphs, they introduced the matching energy of the graph Gn, which was defined as the sum of the absolute values of the eigenvalues of the matching polynomial of the graph Gn. For the Erdös-Rényi type random graph Gn,p of order n with a fixed probability p, where p is a real number greater than zero and less than 1, that is, the graph G on n vertices by connecting two vertices with probability p(e), and each edge is independent of other one. Chen, Li and Lian solved a conjecture proposed by Gutman and Wagner, that is, the expectation of the matching energy of Gn,p converges to a certain number associated with n and p almost surely. But they only did the result for random bipartite graphs. In this paper, we give some lower bounds for the matching energy of random bipartite graphs. And then we will use Chen et al’s method to generalize this conclusion to any random multipartite graphs.
Keywords
Random Graphs, Matching Energy, Multipartite Graphs
To cite this article
Caibing Chang, Bo Deng, Haizhen Ren, Feng Fu, The Matching Energy of Random Multipartite Graphs, American Journal of Mathematical and Computer Modelling. Vol. 4, No. 4, 2019, pp. 94-98. doi: 10.11648/j.ajmcm.20190404.12
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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