(2, 1)-Total Labeling of Trees with Maximum Degree 4

AbstractIt was known that every tree T with maximum degree Δ has Δ+1≤λ2T(T)≤Δ+2. In [14], Wang and Chen characterize completely the (2,1)-total labelling number of trees with maximum degree 3. In this paper, we characterize the (2,1)-total labelling number of trees with maximum degree 4. Let T be a tree with Δ=4 that is not a star. If T is not a generalized star and contains no this figure of a 4-vertex adjacent to three ot her 4-vertices, then T contains one of the particular configurations