A new sufficient condition for a tree T to have the (2, 1)-total number $$\Delta +1$$ Δ + 1

Qiaojun Shu (), Weifan Wang and Yiqiao Wang
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Qiaojun Shu: Hangzhou Dianzhi University
Weifan Wang: Zhejiang Normal University
Yiqiao Wang: Beijing University of Chinese Medicine

Journal of Combinatorial Optimization, 2017, vol. 33, issue 3, No 13, 1020 pages

Abstract: Abstract A k-(2, 1)-total labelling of a graph G is a mapping $$f: V(G)\cup E(G)\rightarrow \{0,1,\ldots ,k\}$$ f : V ( G ) ∪ E ( G ) → { 0 , 1 , … , k } such that adjacent vertices or adjacent edges receive distinct labels, and a vertex and its incident edges receive labels that differ in absolute value by at least 2. The (2, 1)-total number, denoted $$\lambda _2^t(G)$$ λ 2 t ( G ) , is the minimum k such that G has a k-(2, 1)-total labelling. Let T be a tree with maximum degree $$\Delta \ge 7$$ Δ ≥ 7 . A vertex $$v\in V(T)$$ v ∈ V ( T ) is called major if $$d(v)=\Delta $$ d ( v ) = Δ , minor if $$d(v)

Keywords: (2; 1)-total labelling; (2; 1)-total number; Tree; Maximum degree (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-016-0021-0

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