数学季刊 >

2025 , Vol. 40 >Issue 1: 49 - 58

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2025.01.005

路和圈的幂图的Wiener指标

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  • School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, China
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.
LIU Sai-hua (1982-), female, native of Hengdong, Hunan, associate professor of Wuyi University, engages in graph theory;

收稿日期: 2024-08-13

  网络出版日期: 2025-03-30

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).

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On Wiener Index of Power of Paths and Cycles

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  • School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, China
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.
LIU Sai-hua (1982-), female, native of Hengdong, Hunan, associate professor of Wuyi University, engages in graph theory;

Received date: 2024-08-13

  Online published: 2025-03-30

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).

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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 Gk of 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

本文引用格式

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

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 Gk of 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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