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

Xingchao Deng, Zhiwei Shao, Huan Zhang and Weihua Yang

Applied Mathematics and Computation, 2019, vol. 361, issue C, 484-492

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.

Keywords: (d, 1)-total number; Sierpiński graph S(n, k); Sierpiński gasket graph Sn; S+(n,k); S++(n,k) (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:361:y:2019:i:c:p:484-492

DOI: 10.1016/j.amc.2019.05.050

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