Welcome to the Degree-4 census. This site will provide information about edge-transitive graphs of degree 4. This second edition shows graphs of up to 150 vertices. It is known to be incomplete in a few ways. We hope, eventually, to expand the range up to 512 vertices (to include Bouwer's generalization of the Gray Graph), and we invite your comments and contributions.
The main part of the census is the Table . This is a list of all graphs in the census, telling the name, the size of the symmetry group, girth, diameter and other information. Each line has a link to an individual page for that graph, with more information about the graph. A spreadsheet version of the Table is available. Notation, definitions, vocabulary can be found in the Glossary . Summaries of the contributions of individual constructions is available at Families .
The Census is joint work of Steve Wilson at Northern Arizona University, and Primož Potočnik Department of Mathematics, University of Auckland, New Zealand. Acknowledgements:
Thanks to Marston Conder for providing us with the census of 3-valent graphs in MAGMA form!
Many thanks to Alen Orbanič for making available his census of rotary maps with up to 500 edges. We haven't yet incorporated this catalogue and resulting graphs into this Census; that is next in the Plan.
And a sharp-eye award to Rui Duarte for noticing we hadn't included the third family of toroidal maps. (We now have.)
20 June 2005: Posted C4Site for the first time. It has graphs of up to 100 vertices.
8 August 2005: Included consistent cycle information.
25 August 2005: Included generalized Ivanov vectors.
23 January 2008: Included the third torus family, the LR structures RC and SoP, and the first glimmerings of the BGCG not-yet-Construction. Expanded the Census to graphs of order 150.
4 March 2008 Included BW graphs and semi-regular actions.
14 April 2008 Included DG, HC, MSY, MSX, GPS2 graphs. Added Cyclic Coverings from semi-regular actions. Check this out in the Glossary first!
21 April 2008 Modified the description and implementation of BW graphs following a suggestion by Tomaž Pisanski, Corrrected a programming flaw in the BC graphs.
13 February 2010 Corrected a programming flaw that prevented the inclusion of some barrels and another that prevented the inclusion of some PL(R_2m(m+2, m+1))'s.