Characterization Results for theL(2, 1, 1)-Labeling Problem on Trees

• Autorzy: Xiaoling Zhang , Kecai Deng
• Języki publikacji: EN

Abstrakty

EN

An L(2, 1, 1)-labeling of a graph G is an assignment of non-negative integers (labels) to the vertices of G such that adjacent vertices receive labels with difference at least 2, and vertices at distance 2 or 3 receive distinct labels. The span of such a labelling is the difference between the maximum and minimum labels used, and the minimum span over all L(2, 1, 1)-labelings of G is called the L(2, 1, 1)-labeling number of G, denoted by λ2,1,1(G). It was shown by King, Ras and Zhou in [The L(h, 1, 1)-labelling problem for trees, European J. Combin. 31 (2010) 1295–1306] that every tree T has Δ2(T) − 1 ≤ λ2,1,1(T) ≤ Δ2(T), where Δ2(T) = maxuv∈E(T)(d(u) + d(v)). And they conjectured that almost all trees have the L(2, 1, 1)-labeling number attain the lower bound. This paper provides some sufficient conditions for λ2,1,1(T) = Δ2(T). Furthermore, we show that the sufficient conditions we provide are also necessary for trees with diameter at most 6.

Słowa kluczowe

EN

L(2, 1, 1)-labeling; tree; diameter

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2017
• Tom: 37
• Numer: 3
• Strony: 611-622

Daty

wydano

2017-08-01

otrzymano

2015-09-13

poprawiono

2016-05-27

zaakceptowano

2016-05-27

online

2017-07-06

Twórcy

autor

Xiaoling Zhang

• , , , Fujian, P.R.

autor

Kecai Deng

• , , , Fujian, P.R.

Identyfikatory

DOI

10.7151/dmgt.1935