Maximum Estrada Index of Bicyclic Graphs

preprint2012arXivOpen access

Abstract

Let GG be a simple graph of order nn, let λ1(G),λ2(G),...,λn(G)λ_1(G),λ_2(G),...,λ_n(G) be the eigenvalues of the adjacency matrix of GG. The Esrada index of GG is defined as EE(G)=∑i=1neλi(G)EE(G)=\sum_{i=1}^{n}e^{λ_i(G)}. In this paper we determine the unique graph with maximum Estrada index among bicyclic graphs with fixed order.

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