华东师范大学学报(自然科学版) ›› 2014, Vol. 2014 ›› Issue (4): 39-42.

• 应用数学与基础数学 • 上一篇    下一篇

给定权集的赋权双圈图的谱半径

李 丹, 王国平   

  1. 新疆师范大学~~数学科学学院, 乌鲁木齐 830054
  • 收稿日期:2013-08-01 修回日期:2013-11-01 出版日期:2014-07-25 发布日期:2014-07-25

On the spectral radius of weighted bicyclic graphs with a positive weight set

LI Dan, WANG Guo-ping   

  1. School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830054, China
  • Received:2013-08-01 Revised:2013-11-01 Online:2014-07-25 Published:2014-07-25

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摘要： 令$\mathbb{B}^W_{n,n+1}$表示阶为$n$的赋权双圈图的集合,
$W=\{w_1,w_2,\ldots,w_{n+1}\}$, 其中$w_1\geqslant w_2\geqslant\cdots
\geqslant w_{n+1}>0$为权集合.
本文确定了它们中谱半径最大的赋权双圈图的结构及部分权值的分布情况.

关键词: 赋权双圈图, 谱半径, 最大图

Abstract: Let $\mathbb{B}^W_{n,n+1}$ denote the set of bicyclic
weighted graphs of order $n$ with the weight set $W$. In this
article we determine the structure and some weight distribution of
the weighted bicyclic graph with the largest spectral radius in
$\mathbb{B}^W_{n,n+1}$ with a fixed weight set
$W=\{w_1,w_2,\ldots,w_{n+1}\}$, where $w_1\geqslant w_2\geqslant
\cdots \geqslant w_{n+1}>0$.

Key words: weighted bicyclic graph, spectral radius, maximum graph

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