@article {IOPORT.06249562,
author = {Ba\v{c}a, Martin and Numan, Muhammad and Shabbir, Ayesha},
title = {Labelings of type $(1,1,1)$ for toroidal fullerenes.},
year = {2013},
journal = {Turkish Journal of Mathematics},
volume = {37},
number = {6},
issn = {1300-0098},
pages = {899-907},
publisher = {Scientific and Technical Research Council of Turkey (T\"UBITAK), Ankara},
abstract = {Summary: In this paper we deal with the problem of labeling the vertices, edges, and faces of a toroidal fullerene $\Bbb H_{m}^{n}$ with $mn$ hexagons by the consecutive integers from 1 up to $|V(\Bbb H_{m}^{n})| + |E(\Bbb H_{m}^{n})| +|F(\Bbb H_{m}^{n})|$ 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. The paper examines the existence of such labelings for several differences $d$.},
identifier = {06249562},
}