Chinese Quarterly Journal of Mathematics ›› 2025, Vol. 40 ›› Issue (1): 49-58.doi: 10.13371/j.cnki.chin.q.j.m.2025.01.005

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On Wiener Index of Power of Paths and Cycles

  

  1. School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, China
  • Received:2024-08-13 Online:2025-03-30 Published:2025-03-30
  • Contact: LIU Sai-hua E-mail:lsh1808@163.com
  • About author:LIU Sai-hua (1982-), female, native of Hengdong, Hunan, associate professor of Wuyi University, engages in graph theory; LI Xiao-rong (2001-), female, native of Jiangmen, Guangdong, graduate student of Wuyi University, engages in graph theory.
  • Supported by:
    Supported by National Natural Science Foundation of China (Grant No. 12201471) and the Special Foundation in Key Fields for Universities of Guangdong Province (Grant No. 2022ZDZX1034).

Abstract: The Wiener index of a graph is defined to be the sum of the distances of all pairs of vertices in the graph. The kth power Gof a graph G is the graph on V (G) and two vertices are adjacent if and only if their distance in G is less or equal to k. In this paper, we computed the Wiener index of the kth power of paths and cycles for any k ≥2.

Key words: Wiener index, kth power of a path, kth power of a cycle

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