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Labelings of type (1, 1, 1) for toroidal fullerenes

Abstract:

In this paper we deal with the problem of labeling the vertices, edges, and faces of a toroidal fullerene H with rnn hexagons by the consecutive integers from 1 up to |V(Hnm)| + |£(Hnm)| + |F(Hnm)| in such a way that the set of face-weights of 6-sided faces forms an arithmetic progression with common difference d, where by face-weight we mean the sum of the label of that face and the labels of vertices and edges surrounding that face. © Tübi̇tak.