| 单圈图的最大Balaban指数与最大和Balaban指数 |
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| 引用本文： | 尤利华,董欣.单圈图的最大Balaban指数与最大和Balaban指数[J].数学研究及应用,2014,34(4):392-402. |
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| 作者姓名： | 尤利华 董欣 |
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| 作者单位： | 华南师范大学数学科学学院，广东 广州 510631;华南师范大学数学科学学院，广东 广州 510631 |
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| 基金项目： | 广州市珠江科技新星项目(Grant No.2011J2200090), 广东省国际科技合作创新平台项目(Grant No.2012gjhz0007). |
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| 摘 要： | The Balaban index of a connected graph G is defined as J(G) =|E(G)|μ + 1∑e=uv∈E(G)1√DG(u)DG(v),and the Sum-Balaban index is defined as SJ(G) =|E(G)|μ + 1∑e=uv∈E(G)1√DG(u)+DG(v),where DG(u) =∑w∈V(G)dG(u, w), and μ 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.
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| 关 键 词： | 单圈图 连接图 危险品 定义 UV 圈数 顶点 |
| 收稿时间： | 5/5/2013 12:00:00 AM |
| 修稿时间： | 2014/1/28 0:00:00 |
The Maximum Balaban Index (Sum-Balaban Index) of Unicyclic Graphs |
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| Lihua YOU and Xin DONG.The Maximum Balaban Index (Sum-Balaban Index) of Unicyclic Graphs[J].Journal of Mathematical Research with Applications,2014,34(4):392-402. |
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| Authors: | Lihua YOU and Xin DONG |
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| Institution: | School of Mathematical Sciences, South China Normal University, Guangdong 510631, P. R. China;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. |
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| Keywords: | Balaban index Sum-Balaban index unicyclic maximum |
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