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The (d, 1)-total labelling of Sierpin´ski-like graphs

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  • Deng, Xingchao
  • Shao, Zhiwei
  • Zhang, Huan
  • Yang, Weihua

Abstract

A (d, 1)-total labelling of a simple graph G is an assignment of integers to V(G) ∪ E(G) such that any two adjacent vertices of G receive distinct integers, any two adjacent edges of G receive distinct integers, and a vertex and an edge that are incident in G receive integers that differ by at least d in absolute value. The span of a (d, 1)-total labellingof G is the maximum difference between any two labels. The (d, 1)-total number of G, λdT(G), is the minimum span for which G is (d, 1)-total labelled. In this paper, the (d, 1)-total labellingof the Sierpin´ski graph S(n, k), Sierpin´ski gasket graph Sn, graphs S+(n,k) and S++(n,k) are studied, and all of λdT(S(n,k)),λdT(Sn),λdT(S+(n,k)) and λdT(S++(n,k)) for d ≥ k, are obtained.

Suggested Citation

  • Deng, Xingchao & Shao, Zhiwei & Zhang, Huan & Yang, Weihua, 2019. "The (d, 1)-total labelling of Sierpin´ski-like graphs," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 484-492.
    • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:484-492
    DOI: 10.1016/j.amc.2019.05.050
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    References listed on IDEAS

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    1. Luo, Chunmei & Zuo, Liancui, 2017. "Metric properties of Sierpin´ski-like graphs," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 124-136.
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    1. Chunmei Luo & Liancui Zuo & Philip B. Zhang, 2018. "The Wiener index of Sierpiński-like graphs," Journal of Combinatorial Optimization, Springer, vol. 35(3), pages 814-841, April.

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