Journal of East China Normal University(Natural Sc ›› 2014, Vol. 2014 ›› Issue (4): 39-42.

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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

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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