Computing the Kirchhoff Index of Some xyz-Transformations of Regular Molecular Graphs

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• 作者：Yujun Yang (18) (19)
  
• 关键词：regular graph ; resistance distance ; xyz -transformation ; Kirchhoff index ; Laplacian matrix
• 刊名：Lecture Notes in Computer Science
• 出版年：2014
• 出版时间：2014
• 年：2014
• 卷：8588
• 期：1
• 页码：173-183
• 全文大小：256 KB
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• 作者单位：Yujun Yang (18) (19)
  
  18. School of Mathematics, Shandong University, Jinan, Shandong, 250100, P.R. China
  19. School of Mathematics and Information Science, Yantai University, Yantai, Shandong, 264005, P.R. China
  
• ISSN：1611-3349

文摘

Let G be a connected molecular graph. The resistance distance between any two vertices of G is defined as the effective resistance between the two corresponding nodes in the electrical network constructed from G by replacing each edge of Gwith a unit resistor. The Kirchhoff index of G is defined as the sum of resistance distances between all pairs of vertices. Gao et al. (2012) and You et al. (2013) gave formulae for the Kirchhoff index of two types of xyz -transformations, namely, the subdivision graph and the total graph, of regular graphs. In this paper, we compute the Kirchhoff index of some other xyz -transformations of regular (molecular) graphs, with explicit formulae for the Kirchhoff index of these transformation graphs being given in terms of parameters of the original graph.