三圈图的Mostar指标的下界

doi:10.6040/j.issn.1671-9352.0.2023.422

《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (8): 68-77.doi: 10.6040/j.issn.1671-9352.0.2023.422

• • 上一篇

三圈图的Mostar指标的下界

王辉,刘蒙蒙^*

兰州交通大学数理学院, 甘肃兰州 730070

发布日期:2025-07-25
通讯作者: 刘蒙蒙(1986— ),女,教授,博士,研究方向为图论及其应用. E-mail:liumm05@163.com
作者简介:王辉(1998— ),男,硕士研究生,研究方向为图论及其应用. E-mail:wanghui0132022@163.com*通信作者:刘蒙蒙(1986— ),女,教授,博士,研究方向为图论及其应用. E-mail:liumm05@163.com
基金资助:
国家自然科学基金资助项目(11961040)

Lower bound of Mostar index with respect to tricyclic graphs

WANG Hui, LIU Mengmeng^*

School of Mathematics and Science, Lanzhou Jiaotong University, Lanzhou 730070, China

Published:2025-07-25

摘要/Abstract

摘要： 连通图G的Mostar指标M(G)的定义为 M(G)=∑_e=uv∈E(G)|n_u(e)-n_v(e)|,其中n_u(e)表示图G中到点u的距离比到点v的距离近的顶点的数目,n_v(e)表示图G中到点v的距离比到点u的距离近的顶点的数目。得到了连通三圈图的Mostar指标的下界, 刻画了相应的极值图。

关键词: Mostar 指标, 三圈图, 极值图

Abstract: The Mostar index M(G) of a connected graph G is defined as M(G)=∑_e=uv∈E(G)|n_u(e)-n_v(e)|, where n_u(e) and n_v(e) are, respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u. The lower bound of the Mostar index among all tricyclic graphs is established, and the extremal graphs that attained the lower bound are determined.

Key words: Mostar index, tricyclic graph, extremal graph

中图分类号:

O157.5

王辉,刘蒙蒙. 三圈图的Mostar指标的下界[J]. 《山东大学学报(理学版)》, 2025, 60(8): 68-77.

WANG Hui, LIU Mengmeng. Lower bound of Mostar index with respect to tricyclic graphs[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(8): 68-77.

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三圈图的Mostar指标的下界

Lower bound of Mostar index with respect to tricyclic graphs

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