2012/06/23 by Anthony D. Forbes, Forbes, Anthony D.
Computer Science · Engineering · Mathematics · #05B05 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph Labeling and Dimension Problems #graph theory and CDMA systems #math.CO #msc:05B05
paper · pdf · doi:10.48550/arxiv.1207.3032
92 pages. References updated, pictures added, typos corrected. Abridged version omitting all design details accepted by Utilitas Mathematica
openalex publication_date 2012/06/23 · arxiv created 2015/11/06 · arxiv updated 2015/11/09 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
The main aim of this paper is to solve the design spectrum problem for Tietze's graph, the two 18-vertex Blanusa snarks, the six snarks on 20 vertices (including the flower snark J5), the twenty snarks on 22 vertices (including the two Loupekine snarks) and Goldberg's snark 3. Together with the Petersen graph (for which the spectrum has already been computed) this list includes all non-trivial snarks of up to 22 vertices. We also give partial results for a selection of larger graphs: the two Celmins-Swart snarks, the 26- and 34-vertex Blanusa snarks, the flower snark J7, the double star snark, Zamfirescu's graph, Goldberg's snark 5, the Szekeres snark and the Watkins snark.