The research of (2,1)-total labelling of trees basen on Frequency Channel Assignment problem
Haina Sun · MATEC Web of Conferences · 2015
Let T be a tree, Let DΔ(T) denote the set of integers k for which there exist two distinct vertices of maximum degree of distance at k in T. 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 the edges of G such that no two adjacent vertices have the same label, no two adjacent edges have the same label and the difference between the labels of a vertex and its incident edges is at least 2. In this paper, we prove that if T is a tree with Δ≥5 and 3,4∉DΔ(T), then T is Type 1.