The Maximum Balaban Index (Sum-Balaban Index) of Unicyclic Graphs
Received:May 05, 2013  Revised:January 28, 2014
Key Words: Balaban index   Sum-Balaban index   unicyclic   maximum.  
Fund Project:Supported by 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 
Xin DONG School of Mathematical Sciences, South China Normal University, Guangdong 510631, P. R. China 
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Abstract:
      The Balaban index of a connected graph $G$ is defined as $$J(G)=\frac{|E(G)| }{\mu +1}\sum_{e=uv\in E(G)}\frac{1}{{^{\sqrt{D_{G}(u)D_{G}(v)}}} },$$ and the Sum-Balaban index is defined as $$SJ(G)=\frac{|E(G)| }{\mu 1}\sum_{e=uv\in E(G)}\frac{1}{{^{\sqrt{D_{G}(u) D_{G}(v)}}} }, $$ where $D_{G}(u)=\sum_{w\in V(G)}d_{G}(u,w),$ and $\mu$ is the cyclomatic number of $G$. In this paper, the unicyclic graphs with the maximum Balaban index and the maximum Sum-Balaban index among all unicyclic graphs on $n$ vertices are characterized, respectively.
Citation:
DOI:10.3770/j.issn:2095-2651.2014.04.002
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