%0 Journal Article
%T On L(d,1)-labelling of Trees
%J Mathematics Interdisciplinary Research
%I University of Kashan
%Z 2538-3639
%A Hrastnik, Irena
%A Žerovnik, Janez
%D 2020
%\ 06/01/2020
%V 5
%N 2
%P 87-102
%! On L(d,1)-labelling of Trees
%K L(d,1)-labelling
%K tree
%K Distance
%K Δ-vertex
%R 10.22052/mir.2020.227370.1211
%X 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.
%U https://mir.kashanu.ac.ir/article_108519_7a815e176ecf64051ff8ea4e1a552bac.pdf