Abstract
The Estrada index of a graph G, introduced by Estrada in 2000, is defined as EE(G)=∑i=1neλi, where λ1,λ2,…,λn are the eigenvalues of a graph 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.
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