路与路的联图P_m∨P_n的(2,1)-全标号

The Total Labelling of the Unite of Path and Path Graphs

图G的一个k-(2,1)-全标号是一个映射f:V(G)∪E(G)→{1,2,…,k}使得相邻的顶点标不同的号;相邻的边标不同的号;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λ2T(G)定义为G有一个k-(d,1)-全标号的最小的k值。研究路与路的联图Pm∨Pn的(2,1)-全标号问题,并给出Pm∨Pn的(d,1)-全标号数的上界。

The （ d, 1 ） - total labelling number λ2^T （G） 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：any two adjacent vertices of G receive distinct integers, any two adjacent edges of G receive distinct integers, and each vertex and its incident edge receive integers which differ as at least d（ d ≥2） in absolute value. The problem of （ d, 1 ） - total labelling number for the unite of path and path graphs was studied and show some results upper bounds of （d, 1 ） - total labelling number for the unite of path and path graphs.