直积图P_m∧S_n、P_m∧F_n与P_m∧W_n的第一类弱全染色

On a Number of the First Weak Total Coloring of Direct Product Graph P_m∧S_n,P_m∧F_n and P_m∧W_n

图染色是图论的重要组成部分,它有着一定的理论意义和实际应用背景.给出了直积图P_m∧S_n、P_m∧F_n与P_m∧W_n的第一类弱全染色数,并分别给出了构造性的证明,进而验证了这些图对第一类弱全染色猜想成立.

Graph coloring is an important part of the graph theory,which has a certain theoretical and practical application background.In this paper,we give the first kind weakly total coloring number of direct product graph Pm ∧Sn,Pm ∧ Fn and Pm ∧ Wn by using a constructive method,and then verify these graphs to set up the first weak total coloring conjecture.