Note: isometric embeddings of subdivided wheels in hypercubes

Authors:
Sylvain Gravier;Sandi Klavžar;Michel Mollard
Affiliations:
CNRS, GeoD Research Group, Laboratoire Leibniz, 46 Avenue Félix Viallet, 38031 Grenoble Cédex, France;Department of Mathematics PEF, University of Maribor, Koroska 160, 2000 Maribor, Slovenia;CNRS, GeoD Research Group, Laboratoire Leibniz, 46 Avenue Félix Viallet, 38031 Grenoble Cédex, France
Venue:
Discrete Mathematics
Year:
2003

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Abstract

The k-wheel Wk is the graph obtained as a join of a vertex and the cycle of length k. It is proved that a subdivided wheel G embeds isometrically into a hypercube if and only if G is the subdivision graph S(K4) of K4 or G is obtained from the wheel Wk (k ≥ 3) by subdividing any of its outer-edges with an odd number of vertices.