A k-gon α of a polyhedral graph G(V,E,F) is of type ⟨b₁,b₂,...,bₖ⟩ if the vertices incident with α in cyclic order have degrees b₁,b₂,...,bₖ and ⟨b₁,b₂,...,bₖ⟩ is the lexicographic minimum of all such sequences available for α. A polyhedral graph G is oblique if it has no two faces of the same type. Among others it is shown that an oblique graph contains vertices of degree 3.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1157,
author = {Andrey A. Dobrynin and Leonid S. Melnikov and Jens Schreyer and Hansjoachim Walther},
title = {Some news about oblique graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {22},
year = {2002},
pages = {39-50},
zbl = {1011.05040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1157}
}
Andrey A. Dobrynin; Leonid S. Melnikov; Jens Schreyer; Hansjoachim Walther. Some news about oblique graphs. Discussiones Mathematicae Graph Theory, Tome 22 (2002) pp. 39-50. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1157/
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