路与扇形图联图的(2,1)-全标号

图G的一个k-(2,1)-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2.图G的(2,1)-全标号数定义为G有一个k-(2,1)-全标号的最小的k值,记为λT2(G).根据路与扇图联图的特点,找到一种特殊的标号方法,给出路与简单扇图联图的(2,1)-全标号数的上界.

The total labelling number of the joint graph of path and fan

The (2,1)-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 that differ by at least 2 in absolute value. Some results of (2,1)- total labelling number for is given. Key words: joint graphs; (2,1)- total labelling; (2,1)- total labelling number.