Zero(total)forcing number of trees and unicycle graphs
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.
zero forcing numbertotal forcing numbertreeunicycle graph
万方数据
维普
