小直径单圈与双圈图的 Mostar 指标与不规则度的差

数学理论与应用 ›› 2022, Vol. 42 ›› Issue (1): 65-84.

小直径单圈与双圈图的 Mostar 指标与不规则度的差

吴廷增 ^∗，曾晓琳

青海民族大学数学与统计学院, 西宁, 青海, 810007

出版日期:2022-03-31 发布日期:2022-03-31

The Difference of Mostar Index and Irregularity of Unicyclic and Bicyclic Graphs with Small Diameter

Wu Tingzeng^∗， Zeng Xiaolin

School of Mathematics and Statistics, Qinghai Minzu University, Xining 810007, China

Online:2022-03-31 Published:2022-03-31
Contact: Wu Tingzeng(1978−), Professor, PhD；E−mail: mathtzwu@163.com
Supported by:
This work is supported by the National Natural Science Foundation of China (No. 11761056), the Natural Science Foundation of Qinghai Province (No. 2020-ZJ-920), the Scientific Research Innovation Team in Qinghai Minzu University.

摘要/Abstract

摘要： 任给一个连通图, 高芳等人首先引进了~$G$~的一个不变量~$\Delta M(G)=M_{o}(G)-irr(G)$~, 并提出一个问题: 怎样确定所有含~$n$~ 个顶点的连通图~$G$~的~$\Delta M(G)$~的极值, 其中~$M_{o}(G)$~和~$irr(G)$~分别表示~$G$~的~Mostar~指标和不规则度. 本文针对这个问题, 刻画所有直径为3 的单圈图和双圈图~$G$~的~$\Delta M(G)$~ 的上界, 并给出它们的极图.

关键词: Mostar指标, 不规则度, 单圈图, 双圈图, 直径

Abstract:

Let $G$ be a connected graph. Gao et al. first introduced the invariant of $G$: $\Delta M(G)=M_{o}(G)-irr(G)$, and raised a problem: how to determine the extremal graphs among all connected graphs of order $n$ with respect to $\Delta M(G)$, where $M_{o}(G)$ and $irr(G)$ stand for the Mostar index and irregularity of $G$, respectively. In this paper, we characterize the upper bounds of $\Delta M(G)$ over all unicyclic graphs and bicyclic graphs with diameter 3, and determine the extremal graphs.

Key words: Mostar index, Irregular, Unicyclic graph, Bicyclic graph, Diameter

吴廷增, 曾晓琳.

小直径单圈与双圈图的 Mostar 指标与不规则度的差

[J]. 数学理论与应用, 2022, 42(1): 65-84.

Wu Tingzeng, Zeng Xiaolin. The Difference of Mostar Index and Irregularity of Unicyclic and Bicyclic Graphs with Small Diameter[J]. Mathematical Theory and Applications, 2022, 42(1): 65-84.

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