On the Estrada index of cactus graphs

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• 作者：Faxu Li^a ; ^b ; Liang Wei^c ; Haixing Zhao^b ; ^{h.x.zhao@163.com" class="auth_mail" title="E-mail the corresponding author} ; Feng Hu^a ; ^b ; Xiujuan Ma^a ; ^b
• 关键词：Estrada index ; Eigenvalues ; Cactus graph
• 刊名：Discrete Applied Mathematics
• 出版年：2016
• 出版时间：20 April 2016
• 年：2016
• 卷：203
• 期：Complete
• 页码：94-105
• 全文大小：657 K

文摘

The Estrada index   of a graph G$G$, introduced by Estrada in 2000, is defined as $EE\left(G\right)={\sum }_{i=1}^n{e}^{{\lambda }_i}$, where λ₁,λ₂,…,λ_n${\lambda }_1,{\lambda }_2,\dots ,{\lambda }_n$ are the eigenvalues of a graph G$G$. A cactus graph is a connected graph in which any two simple cycles have at most one vertex in common. In this paper, we investigate cactus graphs in which every block is a triangle. The upper and lower bounds for Estrada index of these cactus graphs are obtained, and all the graphs attaining upper and lower bounds are characterized, respectively. The lower bound for Estrada index of these cactus graphs with given maximum degree is also obtained, and graph attaining lower bound is characterized.