An edge grafting theorem on the Estrada index of graphs and its applications. (English) Zbl 1254.05100

Du, Zhibin

Discrete Appl. Math. 161, No. 1-2, 134-139 (2013).

Summary: The Estrada index of a graph \(G\) is defined as \(EE(G)=\sum^n_{i=1}e^{\lambda_i}\), where \(\lambda _{1},\lambda _{2},\dots ,\lambda _{n}\) are the eigenvalues of the adjacency matrix of \(G\). It can be used as an efficient measuring tool in a variety of fields. An edge grafting operation on a graph moves a pendent edge between two pendent paths. In this paper, we give an edge grafting theorem on the Estrada index of graphs. We also give some applications of this theorem.

MSC:

05C50

Graphs and linear algebra (matrices, eigenvalues, etc.)

Keywords:

Estrada index; eigenvalues; adjacency matrix; spectral moments; closed walks; pendent edge; pendent paths; edge grafting operation; grafting theorem