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

LI Dan; WANG Guo-ping

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Jul. 2014

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LI Dan, WANG Guo-ping. On the spectral radius of weighted bicyclic graphs with a positive weight set[J]. Journal of East China Normal University (Natural Sciences), 2014, (4): 39-42.

Citation:

LI Dan, WANG Guo-ping. On the spectral radius of weighted bicyclic graphs with a positive weight set[J]. Journal of East China Normal University (Natural Sciences), 2014, (4): 39-42.

LI Dan, WANG Guo-ping. On the spectral radius of weighted bicyclic graphs with a positive weight set[J]. Journal of East China Normal University (Natural Sciences), 2014, (4): 39-42.

Citation:

LI Dan, WANG Guo-ping. On the spectral radius of weighted bicyclic graphs with a positive weight set[J]. Journal of East China Normal University (Natural Sciences), 2014, (4): 39-42.

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

1.
School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830054, China

Received Date: 2013-08-01
Rev Recd Date: 2013-11-01
Publish Date: 2014-07-25

Abstract

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 $w_1\geqslant w_2\geqslant \cdots \geqslant w_{n+1}0$.
- weighted bicyclic graph,
- spectral radius,
- maximum graph

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References(1)

References

[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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