http://dx.doi.org/10.1016/j.dam.2015.02.019">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

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

Language

English

Abstract

© 2015 Elsevier B.V. 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.

Keywords

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

Publication Date

2015

Source Publication Title

Discrete Applied Mathematics

Volume

187

Start Page

61

End Page

69

Publisher

Elsevier

ISSN (print)

0166218X

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