几类联图的(2,1)-全标号

研究了与频道分配有关的一种染色问题——(p,1)-全标号。图G的(p,1)-全标号是一个映射f:V(G)∪E(G)→{0,1,…,k},使得:G的任两个相邻的顶点得到不同的整数;G的任两个相邻的边得到不同的整数;任一个点和与它相关联的边得到的整数至少相差p。(p,1)-全标号的跨度是指两个标号差的最大值。图G的(p,1)-全标号的最小跨度叫(p,1)-全标号数,记作λTp(G)。根据联图的特征,利用穷染法,得到了几类联图的(2,1)-全标号数。

(2,1)-Total Labelling of Some Join-Graphs

We study the （p,1）-total labelling of graph G,which is related to the frequency assignment problem of the coloring problem.The （p,1）-total labelling of is an assignment f from the set V（G） ∪ E（G） to the integer set 0,1,2,…,k],such that：any two adjacent vertices of G receive distinct integers ; any two adjacent edges of G receive distinct integers; and a vertex and its incident edge receive integers that differ at least p in absolute value.The span of a （p,1）-total labelling is the maximum difference between two labels.The minimum span of a （p,1）-total labelling of G is called the （p,1）-total number and denoted by λTp （G）.In this paper,the （2,1）-total numbers of some join-graphs are given by the eternal coloring according to their feature.