一类二部图的(d,1)-全标号

The total labelling number of some bipartite graphs

图G的一个k-(d,1)-全标号是一个映射f:V(G)∪E(G)→{0,1,2…,k},使得(1)相邻的顶点标不同的号;(2)相邻的边标不同的号;(3)顶点与所关联的边标号数相差至少为d(d≥2)。图G的(d,1)-全标号数定义为G有一个k-(d,1)-全标号的最小的k值。给出了一类二部图的(d,1)-全标号数。

The （ d, 1）-total labelling number of a graph G is the width of the smallest range of integers that suffices to label the vertices and edges of G such that： （ 1 ） any two adjacent vertices of G receive distinct integers; （2） any two adjacent edges of G receive distinct integers; （3） each vertex and its incident edges receive integers which differ as at least d （ d ≥ 2） in absolute value. Some results of the （ d, 1）-total labelling number for some bipartite graphs wene given.