一个圈与一个完全二部图的直积的L(2,1)-标号

L(2,1)-Labeling of the direct product of a cycle and a complete bipartite graph

通过分类讨论、归纳综合的方法,研究了一个圈与一个完全二部图的直积的L(2,1)-标号问题,得到了以下的结果:(1)当n≥3时,C3×Kn,n的L(2,1)-标号数为3n+1;当n≥3时,C4×Kn,n的L(2,1)-标号数的上界是4n;当n≥3时,C5×Kn,n的L(2,1)-标号数为5n-1;(2)当n≥3,m≥6,m≡0(mod3)时,Cm×Kn,n的L(2,1)-标号数为3n+1;当n≥3,m≥6,m≡1(mod3)或m≡2(mod3)时,Cm×Kn,n的L(2,1)-标号数的上界是4n.

Through the classification discussion, induction method, a cycle and a complete bipartitegraph of di- rect product of L（2,1 ）-labeling problem is studied and the following results are obtained： （1）if n ≥3 the L（2,1 ）- labeling number of C3 x Kn,n is determined as 3n ＋ 1 ;if n ≥3 the upper bound of the L（2,1 ） -labeling number is 4n; if n ≥3 the L（2,1）-labeling number of C5 ×Kn,n is determined as 5n - 1 ; （2）if n ≥3,m ≥6,m≡0.（mod3） the L （ 2,1 ） -labeling number of Ca × Kn,n is determined as 3 n ＋ 1 ; if n ≥ 3, m ≥ 6, m ≡ 1 （ mod3 ） or m ≡ 2 （ mod3 ） the upper bound of the L（2,1 ）-labeling number is 4n.