Abstract
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 language | English |
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Pages (from-to) | 61-69 |
Number of pages | 9 |
Journal | Discrete Applied Mathematics |
Volume | 187 |
DOIs | |
Publication status | Published - 31 May 2015 |
Scopus Subject Areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics
User-Defined Keywords
- (2, 1) -total labeling
- Maximum degree
- Tree