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

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.)
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