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Folkman Graph

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FolkmanGraph

The Folkman graph is a semisymmetric graph that has the minimum possible number of nodes (20) (Skiena 1990, p. 186). It is implemented in the Wolfram Language as GraphData["FolkmanGraph"] and illustrated above in several symmetric embeddings.

FolkmanGraphLCF

The Folkman graph has eight distinct generalized LCF notations, three with exponent 5 and five with exponent 1, illustrated above.

The Folkman graph has graph spectrum

(-4)^1(-sqrt(6))^40^(10)(sqrt(6))^44^1.

It has graph genus 3 (Conder and Stokes 2019, Brinkmann 2020).

See also

Edge-Transitive Graph, Gray Graph, Semisymmetric Graph, Symmetric Graph, Vertex-Transitive Graph

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References

Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 235, 1976.Brinkmann, G. "A Practical Algorithm for the Computation of the Genus." 17 May 2020. https://arxiv.org/abs/2005.08243.Conder, M. and Stokes, K. "New Methods for Finding Minimum Genus Embeddings of Graphs on Orientable and Non-Orientable Surfaces." Ars. Math. Contemp. 17, 1-35, 2019.Folkman, J. "Regular Line-Symmetric Graphs." J. Combin. Th. 3, 215-232, 1967.Godsil, C. and Royle, G. Algebraic Graph Theory. New York: Springer-Verlag, p. 36, 2001.Pisanski, T. and Randić, M. "Bridges between Geometry and Graph Theory." In Geometry at Work: A Collection of Papers Showing Applications of Geometry (Ed. C. A. Gorini). Washington, DC: Math. Assoc. Amer., pp. 174-194, 2000.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 186-187, 1990.

Referenced on Wolfram|Alpha

Folkman Graph

Cite this as:

Weisstein, Eric W. "Folkman Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FolkmanGraph.html

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