Mobius梯的(d,1)-全标号

图G 的(d,1)-全标号是从V(G)∪E(G)到非负整数的函数，且满足：(i) G中任意2个相邻顶点的标号不同；(ii) G中任意2个相邻边的标号不同；(iii) 顶点与其关联边的标号差至少为d.(d,1)-全标号的跨度是标号差的最大值. G 的(d,1)-全标号数是G的所有(d,1)-全标号的最小跨度，记为λ^T_d(G).本文完全给出了Mobius梯的(d,1)-全标号数.

(d, 1)-total labelings of the M(o)bius Ladders

A （d,1）-total labeling of a graph G is an assignment of nonnegative integers to V（G） U E（G） such that： （i） any two adjacent vertices of G receive different integers; （ii） any two adjacent edges of G receive different inte- gers; and （iii） a vertex and its incident edge receive integers that differ at least d in absolute value. The span of a （d, 1）-total labeling is the maximum difference between two labels. The （d, 1）-total labeling number of G, denoted by AT （G）, is the minimum span over all （d, 1）-total labelings of G. In this paper, the （d, 1）-total labeling numbers of the Mobius Ladders are given completely for any nonnegative integer d.