@article {
author = {Hrastnik, Irena and Žerovnik, Janez},
title = {On L(d,1)-labelling of Trees},
journal = {Mathematics Interdisciplinary Research},
volume = {5},
number = {2},
pages = {87-102},
year = {2020},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2020.227370.1211},
abstract = {Given a graph G and a positive integer d, an L(d,1)-labelling of G is a function f that assigns to each vertex of G a non-negative integer such that if two vertices u and v are adjacent, then |f(u)-f(v)|≥ d and if u and v are at distance two, then |f(u)-f(v)|≥ 1. The L(d,1)-number of G, λd(G), is the minimum m such that there is an L(d,1)-labelling of G with f(V)⊆ {0,1,… ,m}. A tree T is of type 1 if λd(T)= Δ +d-1 and is of type 2 if λd(T)≥ Δ+d. This paper provides sufficient conditions for λd(T)=Δ+d-1 generalizing the results of Wang [11] and Zhai, Lu, and Shu [12] for L(2,1)-labelling.},
keywords = {L(d,1)-labelling,tree,Distance,Δ-vertex},
url = {https://mir.kashanu.ac.ir/article_108519.html},
eprint = {https://mir.kashanu.ac.ir/article_108519_7a815e176ecf64051ff8ea4e1a552bac.pdf}
}