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s ‐Regular cubic graphs as coverings of the complete bipartite graph K 3,3
Author(s) -
Feng YanQuan,
Kwak Jin Ho
Publication year - 2004
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.10151
Subject(s) - combinatorics , mathematics , bipartite graph , edge transitive graph , symmetric graph , vertex transitive graph , automorphism group , graph automorphism , cubic graph , discrete mathematics , foster graph , line graph , strongly regular graph , graph , automorphism , voltage graph , pathwidth
A graph is s‐regular if its automorphism group acts freely and transitively on the set of s ‐arcs. An infinite family of cubic 1‐regular graphs was constructed in [10], as cyclic coverings of the three‐dimensional Hypercube. In this paper, we classify the s ‐regular cyclic coverings of the complete bipartite graph K 3,3 for each ≥ 1 whose fibre‐preserving automorphism subgroups act arc‐transitively. As a result, a new infinite family of cubic 1‐regular graphs is constructed. © 2003 Wiley Periodicals, Inc. J Graph Theory 45: 101–112, 2004