The Second Largest Balaban Index (Sum-Balaban Index) of Unicyclic Graphs
Received:May 31, 2016  Revised:March 15, 2017
Key Word: Balaban index   Sum-Balaban index   unicyclic graph  
Fund ProjectL:Supported by the Natural Science Foundation of Anhui Province (Grant No.1508085MC55) and the Natural Science Foundation of Educational Government of Anhui Province (Grant No.KJ2013A076).
Author NameAffiliation
Wei FANG School of Instrument and Electronics, North University of China, Shanxi 030051, P. R. China 
Yubin GAO Department of Mathematics, North University of China, Shanxi 030051, P. R. China 
Kai FAN Department of Mathematics, Southeast University, Jiangsu 211189, P. R. China 
Zhongshan LI Department of Mathematics & Statistics, Georgia State University, Atlanta 30302, USA 
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      Balaban index and Sum-Balaban index were used in various quantitative structure-property relationship and quantitative structure activity relationship studies. In this paper, the unicyclic graphs with the second largest Balaban index and the second largest Sum-Balaban index among all unicyclic graphs on $n$ vertices are characterized, respectively.
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