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

作　　者：涂东鑫 李建喜 TU Dong-xin;LI Jian-xi(School of Mathematics and Statistics,Minnan Normal University,Fujian Key Laboratory of Granular Computing and Applications,Zhangzhou 363000,China)

机构地区：[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

出　　处：《高校应用数学学报（A辑）》2024年第3期361-370,共10页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(12171089,12271235);福建省自然科学基金(2021J02048,2023J01909)。

摘　　要：用F(G)和F_(t)(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,F_(t)(T)≥F(T)+1,并刻画了所有满足F_(t)(T)=F(T)+1的树图.Li和Jiang(2022)证明了对任意的单圈图G,F_(t)(G)≥F(G),并刻画了所有满足F_(t)(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F_(t)(T)=F(T)+2的树图和所有满足F_(t)(G)=F(G)+1的局部太阳图.Let F(G)and F_(t)(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,F_(t)(T)≥F(T)+1 and characterized all trees T with F_(t)(T)=F(T)+1.Li and Jiang(2022)proved that for any uncyclic graph G,F_(t)(G)≥F(G),and characterized all unicycle graphs G satisfying F_(t)(G)=F(G).In this paper,all trees T with F_(t)(T)=F(T)+1 and all partial sun graphs G with F_(t)(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 

分 类 号：O157.5[理学—数学]