TY - JOUR
ID - 108519
TI - On L(d,1)-labelling of Trees
JO - Mathematics Interdisciplinary Research
JA - MIR
LA - en
SN - 2538-3639
AU - Hrastnik, Irena
AU - Žerovnik, Janez
AD - Faculty of Mechanical Engineering,
University of Maribor,
Maribor, Slovenia
AD - Faculty of Mechanical Engineering,
University of Ljubljana,
Ljubljana, Slovenia
Y1 - 2020
PY - 2020
VL - 5
IS - 2
SP - 87
EP - 102
KW - L(d,1)-labelling
KW - tree
KW - Distance
KW - Δ-vertex
DO - 10.22052/mir.2020.227370.1211
N2 - 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.
UR - https://mir.kashanu.ac.ir/article_108519.html
L1 - https://mir.kashanu.ac.ir/article_108519_7a815e176ecf64051ff8ea4e1a552bac.pdf
ER -