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 -