给定片段数的树、单圈图和双圈图的极值$p$-谱半径

doi:10.3969/j.issn.1006-8074.2023.03.003

数学理论与应用 ›› 2023, Vol. 43 ›› Issue (3): 61-80.doi: 10.3969/j.issn.1006-8074.2023.03.003

给定片段数的树、单圈图和双圈图的极值$p$-谱半径

邱买容, 贺晓聪^*

中南大学数学与统计学院, 长沙, 410083

出版日期:2023-09-28 发布日期:2023-10-09

The Extremal $p$-spectral Radii of Trees, Unicyclic and Bicyclic Graphs with Given Number of Segments

Qiu Mairong, He Xiaocong*

School of Mathematics and Statistics, Central South University, Changsha 410083, China

Online:2023-09-28 Published:2023-10-09
Supported by:
This work is supported by the Fundamental Research Funds for the Central Universities of Central South University (No. 2021zzts0034)

摘要/Abstract

摘要： 设$G$是一个有限简单图. $S$是$G$的一条途径. 如果$S$的端点(可以相同)在$G$中的度是1或者至少是3, 且其他的顶点在$G$中的度都是2, 则称$S$为$G$的一个片段. 本文对大于1的实数$p$, 分别确定固定阶数和片段数的树、单圈图和双圈图的最大$p$-谱半径, 并刻画对应的极图.

关键词: $p$-谱半径, 树, 单圈图, 双圈图, 片段

Abstract: Let $G$ be a finite and simple graph. A walk $S$ is called a segment of $G$ if the endpoints (not necessarily distinct) of $S$ are of degree 1 or at least 3, and each of the rest vertices is of degree 2 in $G$. In this paper, we determine the graphs that maximize the $p$-spectral radius for $p>1$ among trees, unicyclic and bicyclic graphs with given order and number of segments, respectively.

Key words: $p$-spectral radius, Tree, Unicyclic graph, Bicyclic graph, Segment

邱买容, 贺晓聪. 给定片段数的树、单圈图和双圈图的极值$p$-谱半径[J]. 数学理论与应用, 2023, 43(3): 61-80.

Qiu Mairong, He Xiaocong. The Extremal $p$-spectral Radii of Trees, Unicyclic and Bicyclic Graphs with Given Number of Segments[J]. Mathematical Theory and Applications, 2023, 43(3): 61-80.

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给定片段数的树、单圈图和双圈图的极值$p$-谱半径

The Extremal $p$-spectral Radii of Trees, Unicyclic and Bicyclic Graphs with Given Number of Segments

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