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arXiv 2402.03404math.CO
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关于非传输正则图的$D_α$谱半径

On the $D_α$ spectral radius of non-transmission regular graphs

College of Science, Northwest A&F University（西北农林科技大学理学院）；School of Mathematics and Statistics, Northwestern Polytechnical University（西北工业大学数学与统计学院）

Zengzhao Xu, Weige Xi, Ligong Wang

备注：
This article has undergone further revisions and enhancements, all of which were contributed by Ligong Wang. In recognition of his contributions, Ligong Wang is now acknowledged as a new co-author. The manuscript has been updated to its current version to incorporate these changes. We affirm that all authors have reviewed and approved this update
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AI总结：

本文研究了非传输正则图的D_α谱半径，建立了其与最大顶点传输差值的下界，并确定了达到该下界的极值图。

摘要：

设G是一个阶数为n、边数为m的连通图。令D(G)和Tr(G)分别表示图G的距离矩阵和顶点传输的对角矩阵。对于任意实数α∈[0,1]，定义G的广义距离矩阵D_α(G)为D_α(G)=αTr(G)+(1-α)D(G)。D_α(G)的最大特征值称为G的D_α谱半径或广义距离谱半径，记为μ_α(G)。本文建立了非传输正则图的最大顶点传输与D_α谱半径差值的下界，并刻画了达到该下界的极值图。

英文摘要：

Let $G$ be a connected graph with order $n$ and size $m$. Let $D(G)$ and $Tr(G)$ be the distance matrix and diagonal matrix with vertex transmissions of $G$, respectively. For any real $α\in[0,1]$, the generalized distance matrix $D_α(G)$ of $G$ is defined as $$D_α(G)=αTr(G)+(1-α)D(G).$$ The largest eigenvalue of $D_α(G)$ is called the $D_α$ spectral radius or generalized distance spectral radius of $G$, denoted by $μ_α(G)$. In this paper, we establish a lower bound on the difference between the maximum vertex transmission and the $D_α$ spectral radius of non-transmission regular graphs, and we also characterize the extremal graphs attaining the bound.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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