New bounds on distance Estrada index of graphs

Articles in Press

Document Type : Original paper

Author

Department of Mathematics, College of Sciences, Shiraz University, Shiraz, 71457-44776, Iran

Abstract

For a connected graph $G$ with vertex set $\{v_1,\ldots,v_n\}$, the distance matrix of $G$, denoted by $D(G)$, is an $n\times n$ matrix with zero main diagonal, such that its $(i,j)$-entry is $d(v_i,v_j)$, where $i\neq j$ and $d(v_i,v_j)$ is the distance between $v_i$ and $v_j$. Let $\theta_1,\ldots,\theta_n$ be the eigenvalues of $D(G)$. The distance Estrada index of $G$ is defined as $DEE(G)=\sum_{i=1}^ne^{\theta_i}$. In this paper we find some new sharp bounds for the distance Estrada index of graphs. Our results improve the previous bounds on the distance Estrada index of graphs.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 10 June 2024

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