Estrada Index of Random Bipartite Graphs

Symmetry

卷:7

Yilun Shang¹ 

[1] Department of Mathematics, Tongji University, Shanghai 200092, China;

关键词: Estrada index;    random graph;    eigenvalues;    limit spectral distribution;   

DOI  :  10.3390/sym7042195

来源: DOAJ

【 摘 要 】

The Estrada index of a graph \(G\) of \(n\) vertices is defined by \(EE(G)=\sum_{i=1}^ne^{\lambda_i}\), where \(\lambda_1,\lambda_2,\cdots,\lambda_n\) are the eigenvalues of \(G\). In this paper, we give upper and lower bounds of \(EE(G)\) for almost all bipartite graphs by investigating the upper and lower bounds of the spectrum of random matrices. We also formulate an exact estimate of \(EE(G)\) for almost all balanced bipartite graphs.

【 授权许可】

Unknown