Geodesic
On graphs with vertices of two colors and groups with 3-transpositions
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 257-262 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider labeled undirected graphs without loops or multiple edges with vertices of two colors. A coloring of a graph $\Gamma_n$ is called odd-connected if the removal of vertices of the first color produces an odd number of connected components. A general formula for the number $t_n$ of odd-connected colorings is found for certain families of embedded graphs $\Gamma_n$. The formula depends on two parameters. In the cases where two graphs in a family can be interpreted as Coxeter graphs for certain groups with 3-transpositions, specific formulas for the numbers $t_n$ are found.
Keywords: labeled graph, graph coloring, generating function, Сoxeter graph, group with 3-transpositions. 
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A. I. Sozutov; I. O. Aleksandrova. On graphs with vertices of two colors and groups with 3-transpositions. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 257-262. http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a24/

[1] V.A. Emelichev, O.I. Melnikov, V.I. Sarvanov, R.I. Tyshkevich, Lektsii po teorii grafov, Nauka; Gl. red. fiz.-mat. lit., M., 1990, 384 pp. | MR

[2] Burbaki N., Gruppy i algebry Li. Gl.IV-VI.: Gruppy, porozhdennye otrazheniyami sistemy kornei, Mir, M., 1972, 334 pp. | MR

[3] Hall J.I., Holroyd F.C., Wilson R.J., “Symplectic geometry and mapping class groups”, Geometrical combinatorics, Milton Keynes,1984, Research Notes in Mathematics, 114, Pitman, London, 1984, 21–33 | MR

[4] Hall J.I., “Graphs, geometry, 3-transpositions, and symplectic $F_2$-transvection groups”, Proc. London Math. Soc. (Ser. 3), 58:1 (1989), 89–111 | DOI | MR | Zbl

[5] Sozutov A.I., “O gruppakh tipa $\Sigma _4$, porozhdennykh 3-transpozitsiyami”, Sib. mat. zhurn., 33:1 (1992), 140–149 | MR | Zbl

[6] Sozutov A.I., Kuznetsov A.A., Sinitsin V.M., “O sistemakh porozhdayuschikh nekotorykh grupp s 3-transpozitsiyami”, Sib. mat. elektr. izv., 10, 285–301 | MR | Zbl

[7] Aschbacher M., 3-transposition groups, Cambridge University Press, Cambridge, 1997, 260 pp. | MR | Zbl

[8] Aleksandrova I.O., “O sistemakh porozhdayuschikh nekotorykh grupp s 3-transpozitsiyami”, Algebra, logika: teoriya i prilozheniya, Tez. dokl. mezhdunar. konf., posvyasch. pamyati V.P. Shunkova, Sib. feder. un-t., Krasnoyarsk, 2013, 14–15

[9] Egorychev G.P., Integralnoe predstavlenie i vychislenie kombinatornykh summ, Nauka, Novosibirsk, 1979, 286 pp.