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数学进展 - 2016, Vol. 45(2): 176-184
研究论文
剖分点—边冠图的电阻距离和Kirchhoff 指标
Some Results of Resistance Distance and Kirchhoff Index of Subdivision Vertex-edge Corona for Graphs

刘群
LIU Qun

1. 兰州大学数学与统计学院, 兰州, 甘肃, 730000;
2. 河西学院数学与统计学院, 张掖, 甘肃, 734000
1. Department of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, P. R. China;
2. School of Mathematics and Statistics, Hexi University, Zhangye, Gansu, 734000, P. R. China

收稿日期: 2015-06-25
2016, Vol. 45(2): 176-184
DOI: 10.11845/sxjz.2015128b


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摘要 图$G$的剖分图$S(G)$是在图$G$的每条边上加一个顶点.这些新添加的点的集合称为$I(G)$. 在三个图$G_{1,$G_{2 和$G_{3的基础上引进了一种新的图运算,称为剖分点—边冠图, 记作$G^{S}_{1}\circ(G^{V}_{2}\cup G^{E}_{3})$, 它由$S(G_{1})$, $|V(G_{1}|$个$G_{2的拷贝和 $|I(G_{1}|$ 个$G_{3的拷贝组成,将$V(G_{1})$ 中的第$i$个顶点和第$i$个$G_{2的拷贝中的每个顶点连接, 同时将$I(G_{1})$ 中的第$i$个顶点和第$i$个$G_{3的拷贝中的每个顶点连接. 本文给出了剖分点—边冠图的电阻距离和Kirchhoff 指标.
Abstract:The subdivision graph $S(G)$ of a graph $G$ is the graph obtained by inserting a new vertex into every edge of $G$. The set of such new vertices is denoted by $I(G)$. The subdivision vertex-edge corona of $G_{1 with $G_{2 and $G_{3, denoted by $G^{S}_{1}\circ(G^{V}_{2}\cup G^{E}_{3})$, is the graph consisting of $S(G_{1})$, $|V(G_{1})|$ copies of $G_{2 and $|I(G_{1})|$ copies of $G_{3 by joining the $i$-th vertex in $V(G_{1})$ to each vertex in the $i$-th copy of $G_{2 and the $i$-th vertex of $I(G_{1})$ to each vertex in the $i$-th copy of $G_{3. In this paper, formulae for resistance distance and Kirchhoff index of $G^{S}_{1}\circ(G^{V}_{2} \cup G^{E}_{3})$ are obtained.
PACS:  O157.5  
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