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Resistance Distance and Kirchhoff Index of a Class of Join Graphs

Resistance Distance and Kirchhoff Index of a Class of Join Graphs
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摘要 For some complicated graphs obtained by graph operations,it is very difficult to compute resistance distance and Kirchhoff index.Define a new graph operation,and obtain a class of new join graphs:the subdivision-vertex-vertex join G_1* G_2.Then,describe the Laplacian matrix of the graph G_1 * G_2 and use generalized inverse of the Laplacian matrix to get formulas for resistance distance and Kirchhoff index.Through the obtained formulas,the resistance distance of any pairs of vertices and Kirchhoff index of the join graph can be computed. For some complicated graphs obtained by graph operations,it is very difficult to compute resistance distance and Kirchhoff index.Define a new graph operation,and obtain a class of new join graphs：the subdivision-vertex-vertex join G_1＊ G_2.Then,describe the Laplacian matrix of the graph G_1 ＊ G_2 and use generalized inverse of the Laplacian matrix to get formulas for resistance distance and Kirchhoff index.Through the obtained formulas,the resistance distance of any pairs of vertices and Kirchhoff index of the join graph can be computed.
作者 卢鹏丽 张腾
机构地区 School of Computer and Communication
出处 《Journal of Donghua University(English Edition)》 EI CAS 2016年第5期786-790,共5页 东华大学学报（英文版）
基金 National Natural Science Foundation of China(No.11361033)
关键词 Kirchhoff Laplacian vertex inverse compute operations Distance undirected connected formulas generalized inverse resistance distance Kirchhoff index
分类号 O157 [理学—基础数学]
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Journal of Donghua University(English Edition)
2016年 第5期

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