TY - JOUR
T1 - (2, 1) -total labeling of trees with large maximum degree
AU - Chen, Dong
AU - SHIU, Wai Chee
AU - Shu, Qiaojun
AU - SUN, Pak Kiu
AU - Wang, Weifan
N1 - Publisher Copyright:
© 2015 Elsevier B.V.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2015/5/31
Y1 - 2015/5/31
N2 - A k-(2, 1)-total labeling of a graph G is to label the vertices and the edges of G using integers from 0 to k such that all adjacent vertices as well as edges receive different labels, and the difference between the labels of a vertex and its incident edges is at least 2. The (2,1)-total labeling number λ2t(G) is the smallest integer k such that G has a k-(2, 1)-total labeling. It is known that λ2t(T), where T is a tree with maximum degree Δ, equals to either Δ+1 or Δ+2. In this paper, we provide a sufficient condition for a tree T to have λ2t(T)=Δ+1 when Δ≥9.
AB - A k-(2, 1)-total labeling of a graph G is to label the vertices and the edges of G using integers from 0 to k such that all adjacent vertices as well as edges receive different labels, and the difference between the labels of a vertex and its incident edges is at least 2. The (2,1)-total labeling number λ2t(G) is the smallest integer k such that G has a k-(2, 1)-total labeling. It is known that λ2t(T), where T is a tree with maximum degree Δ, equals to either Δ+1 or Δ+2. In this paper, we provide a sufficient condition for a tree T to have λ2t(T)=Δ+1 when Δ≥9.
KW - (2, 1) -total labeling
KW - Maximum degree
KW - Tree
UR - http://www.scopus.com/inward/record.url?scp=84928213562&partnerID=8YFLogxK
U2 - 10.1016/j.dam.2015.02.019
DO - 10.1016/j.dam.2015.02.019
M3 - Article
AN - SCOPUS:84928213562
SN - 0166-218X
VL - 187
SP - 61
EP - 69
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -