Lalonde Graph
LalondeGraph
The Lalonde graph is the 21-vertex, 72-edge graph given by Lalonde (2025) in connection with rank-r variants of the quantum chromatic number. It satisfies
| chi_q(G)=chi_q^((2))(G)=4 |
and
| xi(G)=chi_q^((1))(G)=chi(G)=5, |
where xi denotes orthogonal rank.
The Lalonde graph gives a separation between the rank-1 and rank-2 quantum chromatic numbers. It is Hamiltonian, nonplanar, and pancyclic.
The Lalonde graph will be implemented in a future version of the Wolfram Language as GraphData ["LalondeGraph"].
See also
Cameron-Montanaro-Newman-Severini-Winter Graph, Chromatic Number, Graph Coloring, Mancinska-Roberson Graphs, Quantum Chromatic Number, Vertex ColoringExplore with Wolfram|Alpha
WolframAlpha
References
Lalonde, O. "On the Quantum Chromatic Numbers of Small Graphs." Elec. J. Combin. 32, No. 1, P1.18, 1-26, 2025. https://doi.org/10.37236/12506.Cite this as:
Weisstein, Eric W. "Lalonde Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LalondeGraph.html