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arXiv · 1908.03893

Bounds on the $\alpha$-distance spectrum of graphs

Yang Yang·Lizhu Sun·Changjiang Bu
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Abstract

For a simple, undirected and connected graph $G$, $D_{\alpha}(G) = \alpha Tr(G) + (1-\alpha) D(G)$ is called the $\alpha$-distance matrix of $G$, where $\alpha\in [0,1]$, $D(G)$ is the distance matrix of $G$, and $Tr(G)$ is the vertex transmission diagonal matrix of $G$. Recently, the $\alpha$-distance energy of $G$ was defined based on the spectra of $D_{\alpha}(G)$. In this paper, we define the $\alpha$-distance Estrada index of $G$ in terms of the eigenvalues of $D_{\alpha}(G)$. And we give some bounds on the spectral radius of $D_{\alpha}(G)$, $\alpha$-distance energy and $\alpha$-distance Estrada index of $G$.

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Yang Yang, Lizhu Sun, Changjiang Bu. 2019-08-11. Bounds on the $\alpha$-distance spectrum of graphs. https://arxiv.org/abs/1908.03893

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