Journal of Integer Sequences, Vol. 25 (2022), Article 22.1.3

Generating All Rigidity Circuits on at Most 10 Vertices and All Assur Graphs on at Most 11 Vertices


Ciaran Mc Glue
Maynooth University (NUI)
Maynooth
Co. Kildare
Ireland

Klara Stokes
Umeå University
Department of Mathematics and Mathematical Statistics
901 87 Umeå
Sweden
and
Maynooth University (NUI)
Maynooth
Co. Kildare
Ireland

Abstract:

We present an inventory and the enumeration of all non-isomorphic rigidity circuits on up to 10 vertices, as well as all non-isomorphic Assur graphs on up to 11 vertices. Assur graphs and Baranov trusses are closely related. We clarify the relation between Baranov trusses and (2,3)-tight graphs on the one hand, and between Assur groups and Assur graphs on the other hand.

Full version:  pdf,    dvi,    ps,    latex,     data and programs for the paper

(Concerned with sequences A227117 A350484 A350485.)

Received August 20 2020; revised versions received September 16 2020; December 31 2021; January 1 2022. Published in Journal of Integer Sequences, January 2 2022.

Return to Journal of Integer Sequences home page