On Wiener Index of Power of Paths and Cycles

LIU Sai-hua, LI Xiao-rong

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

Chinese Quarterly Journal of Mathematics >

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

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

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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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

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

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