树图和单圈图的零强迫数与全强迫数

Zero(total)forcing number of trees and unicycle graphs

涂东鑫 ¹李建喜¹

扫码查看

作者信息

1. 闽南师范大学数学与统计学院,福建省粒计算及其应用重点实验室,福建漳州 363000
折叠

摘要

用F(G)和Ft(G)分别表示图G的零强迫数和全强迫数.Davila(2020)研究了树图的零强迫数与全强迫数的关系,证明了对任意树图T,Ft(T)≥F(T)+1,并刻画了所有满足Ft(T)=F(T)+1的树图.Li和Jiang(2022)证明了对任意的单圈图G,Ft(G)≥F(G),并刻画了所有满足Ft(G)=F(G)的单圈图.该文通过分别刻画全强迫数为3的所有树图和单圈图,进一步刻画了所有满足Ft(T)=F(T)+2的树图和所有满足Ft(G)=F(G)+1的局部太阳图.

Abstract

Let F(G)and Ft(G)be the zero forcing number and the total forcing number of G,respectively.Davila(2020)studied the relationship between the zero forcing number and the total forcing number for a tree,and proved that for any tree T,Ft(T)≥F(T)+1 and characterized all trees T with Ft(T)=F(T)+1.Li and Jiang(2022)proved that for any uncyclic graph G,Ft(G)≥F(G),and characterized all unicycle graphs G satisfying Ft(G)=F(G).In this paper,all trees T with Ft(T)=F(T)+1 and all partial sun graphs G with Ft(G)=F(G)+1 are characterized respectively by determining all trees and unicycle graphs with the total forcing number 3.

关键词

零强迫数/全强迫数/树图/单圈图

Key words

zero forcing number/total forcing number/tree/unicycle graph

引用本文复制引用

基金项目

国家自然科学基金(12171089)

国家自然科学基金(12271235)

福建省自然科学基金(2021J02048)

福建省自然科学基金(2023J01909)

出版年

2024

高校应用数学学报

浙江大学中国工业与应用数学学会

高校应用数学学报

CSTPCD北大核心

影响因子：0.396

ISSN：1000-4424

段落导航