Kirchhoff index of graphs and some graph operations

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• 作者：A NIKSERESHT ; Z SEPASDAR ; M H SHIRDAREH-HAGHIGHI
• 关键词：Kirchhoff index ; resistance distance ; 05C12 ; 05C50
• 刊名：Proceedings Mathematical Sciences
• 出版年：2014
• 出版时间：August 2014
• 年：2014
• 卷：124
• 期：3
• 页码：281-289
• 全文大小：288 KB
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• 作者单位：A NIKSERESHT (1)
  Z SEPASDAR (1)
  M H SHIRDAREH-HAGHIGHI (1)
  
  1. Department of Mathematics, College of Sciences, Shiraz University, 71457-44776, Shiraz, Iran
  
• ISSN：0973-7685

文摘

Let T be a rooted tree, G a connected graph, x, y ?V(G) be fixed and G i ’s be |V(T)| disjoint copies of G with x i and y i denoting the corresponding copies of x and y in G i , respectively. We define the T-repetition of G to be the graph obtained by joining y i to x j for each i ?V(T) and each child j of i. In this paper, we compute the Kirchhoff index of the T-repetition of G in terms of parameters of T and G. Also we study how Kf(G) behaves under some graph operations such as joining vertices or subdividing edges.