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arXiv · 1509.04565

Classification of vertex-transitive cubic partial cubes

Tilen Marc
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Abstract

Partial cubes are graphs isometrically embeddable into hypercubes. In this paper it is proved that every cubic, vertex-transitive partial cube is isomorphic to one of the following graphs: $K_2 \, \square \, C_{2n}$, for some $n\geq 2$, the generalized Petersen graph $G(10,3)$, the cubic permutahedron, the truncated cuboctahedron, or the truncated icosidodecahedron. This classification is a generalization of results of Bre\v{s}ar et al.~from 2004 on cubic mirror graphs, it includes all cubic, distance-regular partial cubes (Weichsel, 1992), and presents a contribution to the classification of all cubic partial cubes.

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Tilen Marc. 2015-09-15. Classification of vertex-transitive cubic partial cubes. https://arxiv.org/abs/1509.04565

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