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Lalonde Graph

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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 Coloring

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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

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