On the spectral radius of weighted bicyclic graphs with a positive weight set
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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.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 $w_1\geqslant w_2\geqslant \cdots \geqslant w_{n+1}0$.
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Key words:
- weighted bicyclic graph /
- spectral radius /
- maximum graph
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[1] {1} YANG H Z, HU G Z, HONG Y. Bounds of spectral radii of weighted tree [J]. Tsinghua Sci Technol, 2003(8): 517-520.{2} TAN S W. On the sharp upper bound of spectral radius of weighted trees [J]. J Math Res Exp, 2009(29): 293-301.{3} TAN S W, YAO Y H. On the spectral radius of weighted trees with fixed diameter and weighted set [J]. Linear Algebra Appl, 2009, 431: 86-98.{4} DAS K C, BAPAT R B. A sharp upper bound on the spectral radius of weighted graphs [J]. Linear Algebra Appl, 2008, 308: 3180-3186.{5} LI S C, TIAN Y. On the spectral radius of weighted unicyclic with a positive weight set [J]. Linear and Multilinear Algebra, 2011, 59: 1399-1407. -
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