最大度是3的2-连通外平面图的(p,1)-全标号

(p,1)-Total Labelling of 2-connected Outerplanar Graphs with Maximum Degree 3

图G的一个(p,1)-全标号是与频率分配有关的一种染色,它是从V(G)∪E(G)到一个整数集合的映射,必须满足:(1)图G的任意两个相邻的顶点得到不同的整数;(2)图G的任意两个相邻的边得到不同的整数;(3)图G的任意一个顶点和它所关联的边得到的整数必须至少相差p.一个(p,1)-全标号的跨度是指最大标号数与最小标号数的差.图G的所有(p,1)-全标号中最小的跨度,称为图G的(p,1)-全标号数,记为λpT(G).本文研究了最大度是3的2-连通外平面图G的全标号数.

A （p, 1 ）-total labelling of a graph G is an assignment of inters to V（G）∪E（G） such as：（1） any two adjacent vertices of G receive distinct integers, （2） any two adjacent edges of G receive distinct integers,and （3） a vertex and its incident edge receive integers that differ by 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 r number and denoted by λ p^T （G）. This paper shows the （p, 1）-total number of 2-connected outerplanar graph with maximum degree 3 .