(2, 1) -total labeling of trees with large maximum degree

Dong Chen, Wai Chee SHIU*, Qiaojun Shu, Pak Kiu SUN, Weifan Wang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)61-69
Number of pages9
JournalDiscrete Applied Mathematics
Publication statusPublished - 31 May 2015

Scopus Subject Areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

User-Defined Keywords

  • (2, 1) -total labeling
  • Maximum degree
  • Tree


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