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Paulus-Rozenfeld-Thompson Graph


Paulus-Rozenfeld-Thompson gGraph

The (26,8)-Paulus graph having the largest possible graph automorphism group order of all 26-node Paulus graphs (namely 120) is sometimes known as the Paulus-Rozenfeld-Thompson graph (or PRT graph for short) and denoted T (Gyürki et al. 2020). It is illustrated above in two embeddings constructed by Gyürki et al. (2020).

PaulusRozenfeldThompsonGraphEmbeddings

Additional embeddings due to Ed Pegg, Jr. (pers. comm., Mar 3, 2021) are illustrated above.

This graph was selected as the logo of the conference "Symmetry Versus Regularity: The First 50 Years Since Weisfeiler-Leman Stabilization" held July 1-7, 2018 in Pilsen, Czech Republic.

Its is implemented in the Wolfram Language as GraphData[{"Paulus", {26, 8}}].


See also

Paulus Graphs

This entry contributed by Ed Pegg, Jr. (author's link)

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References

Gyürki, Š.; Klin, M.; and Ziv-Av, M. "The Paulus-Rozenfeld-Thompson Graph on 26 Vertices Revisited and Related Combinatorial Structures." In Isomorphisms, Symmetry and Computations in Algebraic Graph Theory: Pilsen, Czech Republic, October 3-7, 2016 (Ed. G. A. Jones, I. Ponomarenko, and J. Širáň). Cham, Switzerland: Springer Nature, pp. 73-154, 2020.ITI Center of Excellence, Faculty of Applied Sciences of the University of West Bohemia in Pilsen, Union of Czech Mathematicians and Physicists, Slovak Mathematical Society, and Mathematical Institute of Slovak Academy of Sciences. "Conference in Algebraic Graph Theory Symmetry vs Regularity: The First 50 Years Since Weisfeiler-Leman Stabilization." https://www.iti.zcu.cz/wl2018/.Rozenfel'd, M. Z. "'The Construction and Properties of Certain Classes of Strongly Regular Graphs." Uspehi Mat. Nauk 28, 197-198, 1973.Thompson, D. M. "Design Constructibility: Strongly Regular Graphs and Block Designs." Ph.D. dissertation. Tucson, AZ: University of Arizona, 1979.Thompson, D. M. "Eigengraphs: Constructing Strongly Regular Graphs with Block Designs." Utilitas Math. 20, 83-115, 1981.

Cite this as:

Pegg, Ed Jr. "Paulus-Rozenfeld-Thompson Graph." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Paulus-Rozenfeld-ThompsonGraph.html

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