图的(3,1)-全标号

(3,1)-Total Labeling of Graphs

图G的(p,1)-全标号是对G的点和边进行标号,满足:任意两个相邻的点得到不同的标号,任意两个相邻的边得到的标号也不同。并且任意一个点与和它相关联的边所得到的标号的差的绝对值至少为p,其中在全标号中最大的标号与最小的标号的差值称为全标号的跨度,记一个(p,1)-全标号中最小的跨度为λpT。证明了当p=3,Δ(G)≥9时,λ3T≤2Δ(G)+1。

A （p, 1 ） -total labeling of a graph G is a labeling of vertices and edges, such that any two adjacent vertices of G receive distinct integers, any two adjacent edges receive distinct integers, and a vertex and its incident edges receive integers that differ by at least p in absolute value. The span of a （p, 1）-total labeling is the minimum difference between the maxi-mum label and the minimum label. The minimum span λ^τp is noted when p=3,△（G）≥9,λ^τ3≤2△（G）＋1 is proved.