The Laplacian Spread of Bicyclic Graphs
Received:February 17, 2008  Revised:October 06, 2008
Key Word: bicyclic graph   Laplacian matrix   spread.  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.10601001), the Natural Science Foundation of Anhui Province (Grant No.070412065), Project of Anhui Province for Young Teachers Research Support in Universities (Grant No.2008jql083), Natural Science Foundation of Department of Education of Anhui Province (Grant No.2005kj005zd), Project of Anhui University on Leading Researchers Construction and Foundation of Innovation Team on Basic Mathematics of Anhui University.
Author NameAffiliation
Yi Zheng FAN School of Mathematical Sciences, Anhui University, Anhui 230039, P. R. China 
Shuang Dong LI School of Mathematical Sciences, Anhui University, Anhui 230039, P. R. China 
Ying Ying TAN Department of Mathematics \& Physics, Anhui University of Architecture, Anhui 230022, P. R. China 
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      The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second smallest eigenvalue of the Laplacian matrix of the graph. In our recent work, we have determined the graphs with maximal Laplacian spreads among all trees of fixed order and among all unicyclic graphs of fixed order, respectively. In this paper, we continue the work on Laplacian spread of graphs, and prove that there exist exactly two bicyclic graphs with maximal Laplacian spread among all bicyclic graphs of fixed order, which are obtained from a star by adding two incident edges and by adding two nonincident edges between the pendant vertices of the star, respectively.
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