AUSTRALASIAN JOURNAL OF COMBINATORICS Volume 28 (2003), Pages 217–224 On cubic and edge-critical isometric subgraphs of hypercubes C. Paul Bonnington * Department of Mathematics University of Auckland Auckland, New Zealand p.bonnington@auckland.ac.nz Sandi Klavˇ zar † Department of Mathematics, University of Maribor Koroˇ ska cesta 160 2000 Maribor, Slovenia sandi.klavzar@uni-mb.si Alenka Lipovec Department of Education, University of Maribor Koroˇ ska cesta 160 2000 Maribor, Slovenia alenka.lipovec@uni-mb.si Abstract All cubic partial cubes (i.e., cubic isometric subgraphs of hypercubes) up to 30 vertices and all edge-critical partial cubes up to 14 vertices are presented. The lists of graphs were confirmed by computer search to be complete. Non-trivial cubic partial cubes on 36, 42, and 48 vertices are also constructed. 1 Introduction Partial cubes are, by definition, graphs that admit isometric embeddings into hyper- cubes. They were introduced by Graham and Pollak [9] and first characterized by * Supported by the Marsden Fund (Grant Number UOA-825) administered by the Royal Society of New Zealand. † Supported by the Ministry of Education, Science and Sport of Slovenia under the grant 0101- 504.