路和圈的幂图的Wiener指标

doi:10.13371/j.cnki.chin.q.j.m.2025.01.005

数学季刊 ›› 2025, Vol. 40 ›› Issue (1): 49-58.doi: 10.13371/j.cnki.chin.q.j.m.2025.01.005

路和圈的幂图的Wiener指标

School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, China

收稿日期:2024-08-13 出版日期:2025-03-30 发布日期:2025-03-30
通讯作者: 刘赛华 E-mail:lsh1808@163.com
作者简介: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.
基金资助:
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).

On Wiener Index of Power of Paths and Cycles

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).

摘要/Abstract

摘要： 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 G^kof 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.

关键词: Wiener index, kth power of a path, kth power of a cycle

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 G^kof 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

中图分类号:

O157.5

刘赛华, 李晓蓉. 路和圈的幂图的Wiener指标[J]. 数学季刊, 2025, 40(1): 49-58.

LIU Sai-hua, LI Xiao-rong. On Wiener Index of Power of Paths and Cycles[J]. Chinese Quarterly Journal of Mathematics, 2025, 40(1): 49-58.

路和圈的幂图的Wiener指标

On Wiener Index of Power of Paths and Cycles

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