The Smallest Hosoya Index of Bicyclic Graphs with Given Pendent Vertices
Received:July 03, 2012  Revised:October 12, 2013
Key Words: Hosoya index   bicyclic graph   pendent vertex   matching.  
Fund Project:Supported by National Natural Science Foundation of China (Grant No.11301093), the Zhujiang Technology New Star Foundation of Guangzhou (Grant No.2011J2200090) and Program on International Cooperation and Innovation, Department of Education, Guangdong Province (Grant No.2012gjhz0007).
Author NameAffiliation
Lihua YOU School of Mathematical Sciences, South China Normal University, Guangdong 510631, P. R. China 
Chaoxia WEI School of Mathematical Sciences, South China Normal University, Guangdong 510631, P. R. China 
Zhifu YOU School of Computer Science, Guangdong Polytechnic Normal University, Guangdong 510665, P. R. China 
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Abstract:
      Let $G$ be a graph. The Hosoya index $Z(G)$ of a graph $G$ is defined to be the total number of its matchings. In this paper, we characterize the graph with the smallest Hosoya index of bicyclic graphs with given pendent vertices. Finally, we present a new proof about the smallest Hosoya index of bicyclic graphs.
Citation:
DOI:10.3770/j.issn:2095-2651.2014.01.002
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