Geodesic
On the Estrada Index of Point Attaching Strict $k$-Quasi Tree Graphs
Kragujevac Journal of Mathematics, Tome 44 (2020) no. 2, p. 165

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Let $G=(V,E)$ be a finite and simple graph with $\lambda_1, \lambda_2, …, \lambda_n$ as its eigenvalues. The Estrada index of $G$ is $EE(G)=\sum_{i=1}^{n}e^{\lambda_{i}}$. For a positive integer $k$, a connected graph $G$ is called strict $k$-quasi tree if there exists a set $U$ of vertices of size $k$ such that $G\setminus U$ is a tree and this is as small as possible with this property. In this paper, we define point attaching strict $k$-quasi tree graphs and obtain the graph with minimum Estrada index among point attaching strict $k$-quasi tree graphs with $k$ even cycles.
Classification : 05C35, 05C50
Keywords: Estrada index, quasi tree graph, point attaching strict $k$-quasi tree graph 
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     author = {Mohammad A. Iranmanesh and Raziyeh Nejati},
     title = {On the {Estrada} {Index} of {Point} {Attaching} {Strict} $k${-Quasi} {Tree} {Graphs}},
     journal = {Kragujevac Journal of Mathematics},
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Mohammad A. Iranmanesh; Raziyeh Nejati. On the Estrada Index of Point Attaching Strict $k$-Quasi Tree Graphs. Kragujevac Journal of Mathematics, Tome 44 (2020) no. 2, p. 165 . http://geodesic.mathdoc.fr/item/KJM_2020_44_2_a0/