A Proof of a Conjecture on the Estrada Index

作者：Deng; Hanyuan

来源：MATCH-Communications in Mathematical and in Computer Chemistry, 2009, 62(3): 599-606.

Let G be a graph on n vertices, and lambda(1), lambda(2),...,lambda(n) its eigenvalues. The Estrada index of G is a graph invariant, defined as EE(G) = Sigma(n)(i=1) e(lambda i). In this paper, it is shown that the path P-n and the star S-n have the minimum and the maximum Estrada indices among n-vertex trees, respectively; and the path P-n and the complete graph K-n have the minimum and the maximum Estrada indices among connected graphs of order n, respectively. This proves a conjecture of de la Pena, Gutman and Rada.

• 出版日期2009
• 单位湖南师范大学