Some extremal properties of the resolvent energy, Estrada and resolvent Estrada indices of graphs

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• 作者：Zhongxun Zhu ^{zzxun73@mail.scuec.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Eigenvalue ; Resolvent energy ; Estrada index ; Resolvent Estrada index
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：447
• 期：2
• 页码：957-970
• 全文大小：481 K

文摘

Let G be a simple connected graph on n   vertices and λ₁,λ₂,…,λ_n${\lambda }_1,{\lambda }_2,\dots ,{\lambda }_n$ be the eigenvalues of the adjacency matrix of G. Estrada and Higham proposed an invariant of a graph G   based on Taylor series expansion of spectral moments $EE(G,c)={\sum }_{k=0}^{\infty }{c}_k{M}_k(G)$. For $c_k=\frac{1}{n^k}$ (resp. $\frac{1}{k!}$, $\frac{1}{{(n-1)}^k}$), EE(G,c)$EE(G,c)$ is the Resolvent energy (resp. Estrada index, Resolvent Estrada index) of G. In  and , Gutman et al. conjectured the structure of the extremal members of some classes of graphs by the aid of computer on Resolvent energy and Resolvent Estrada index, respectively. In [1], L. Allem et al. confirmed the validity of some of these conjectures on Resolvent energy. In this paper, we continue to study these indices based on these conjectures.