Estimating the distance Estrada index

Yilun Shang

Abstract


Suppose $G$ is a simple graph on $n$ vertices. The $D$-eigenvalues$\mu_1,\mu_2,\cdots,\mu_n$ of $G$ are the eigenvalues of itsdistance matrix. The distance Estrada index of $G$ is defined as$DEE(G)=\sum_{i=1}^ne^{\mu_i}$. In this paper, we establish newlower and upper bounds for $DEE(G)$ in terms of the Wiener index$W(G)$. We also compute the distance Estrada index for some concretegraphs including the buckminsterfullerene $C_{60}$.

Keywords


Distance degree; distance matrix; Estrada index; Wiener index.

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References


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