1. The (d, 1)-total labelling of Sierpi[formula omitted]ski-like graphs.
- Author
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Deng, Xingchao, Shao, Zhiwei, Zhang, Huan, and Yang, Weihua
- Subjects
- *
GRAPH labelings , *LABELS , *ABSOLUTE value , *INTEGERS - 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 labelling of G is the maximum difference between any two labels. The (d , 1) -total number of G , λ d T (G) , is the minimum span for which G is (d , 1)-total labelled. In this paper, the (d , 1) -total labelling of the Sierpi n ´ ski graph S (n, k), Sierpi n ´ ski gasket graph S n , graphs S + (n , k) and S + + (n , k) are studied, and all of λ d T (S (n , k)) , λ d T (S n) , λ d T (S + (n , k)) and λ d T (S + + (n , k)) for d ≥ k , are obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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