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

摘要

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.