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

Author

Listed:
  • Qiaojun Shu

    (Hangzhou Dianzhi University)

  • Weifan Wang

    (Zhejiang Normal University)

  • Yiqiao Wang

    (Beijing University of Chinese Medicine)

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)

Suggested Citation

  • Qiaojun Shu & Weifan Wang & Yiqiao Wang, 2017. "A new sufficient condition for a tree T to have the (2, 1)-total number $$\Delta +1$$ Δ + 1," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 1011-1020, April.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:3:d:10.1007_s10878-016-0021-0
    DOI: 10.1007/s10878-016-0021-0
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    References listed on IDEAS

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