Geodesic
Classification of the total and regular graphs of three-point sets
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXV, Tome 514 (2022), pp. 167-192 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper studies the structures of the total and regular graphs of sets of three elements over fields of characteristic zero. The graphs themselves are classified up to isomorphism. 
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     author = {V. V. Promyslov},
     title = {Classification of the total and regular graphs of three-point sets},
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V. V. Promyslov. Classification of the total and regular graphs of three-point sets. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXV, Tome 514 (2022), pp. 167-192. http://geodesic.mathdoc.fr/item/ZNSL_2022_514_a9/

[1] E. I. Bunina, A. V. Mikhalev, A. G. Pinus, Elementarnaya i blizkaya k nei logicheskie ekvivalentnosti klassicheskikh i universalnykh algebr, MTsNMO, M., 2015

[2] A. M. Maksaev, V. V. Promyslov, “O totalnom i regulyarnom grafakh mnogochlena”, Fund. prikl. mat., 23:4 (2021), 113–142 | MR

[3] V. V. Promyslov, “Klassifikatsiya regulyarnykh grafov trekhtochechnykh mnozhestv”, Intel. sistemy. Teoriya pril., 25:4 (2021), 205–208 | MR

[4] F. Kharari, Teoriya grafov, Mir, M., 1973

[5] S. Akbari, M. Jamaali, S. A. Seyed Fakhari, “The clique numbers of regular graphs of matrix algebras are finite”, Linear Algebra Appl., 431 (2009), 1715–1718 | DOI | MR

[6] D. F. Anderson, A. Badawi, “The total graph of a commutative ring”, J. Algebra, 320 (2008), 2706–2719 | DOI | MR

[7] S. Akbari, M. Aryapoor, M. Jamaali, “Chromatic number and clique number of subgraphs of regular graph of matrix algebras”, Linear Algebra Appl., 436 (2012), 2419–2424 | DOI | MR

[8] S. Akbari, F. Heydari, “The regular graph of a noncommutative ring”, Bull. Austral. Math. Soc., 89:1 (2014), 132–140 | DOI | MR

[9] P. J. Cameron, “Research problems from the BCC22 ”, Discrete Math., 311 (2011), 1074–1083 | DOI | MR

[10] A. E. Guterman, A. M. Maksaev, V. V. Promyslov, “Pairs of maps preserving singularity on subsets of matrix algebras”, Linear Algebra Appl., 644 (2022), 1–27 | DOI | MR

[11] U. Knauer, K. Knauer, Algebraic Graph Theory: Morphisms, Monoids and Matrices, 2nd Rev. and Ext. ed., de Gruyter, 2015 | MR

[12] I. Tomon, “On the chromatic number of regular graphs of matrix algebras”, Linear Algebra Appl., 475 (2015), 154–162 | DOI | MR

[13] J. Zhou, D. Wong, X. Ma, “Automorphism group of the total graph over a matrix ring”, Linear Multilinear Algebra, 65:3 (2017), 572–581 | DOI | MR