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Trofimov, Vladimir Ivanovich
Head Scientist Researcher
Doctor of physico-mathematical sciences (1992)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
Birth date: 29.03.1957
E-mail:
Keywords: groups; locally finite graphs; automorphisms of graphs; vertex-transitive groups of automorphisms of graphs; vertex stabilizers of graphs; applications to physics.
   
Main publications:
  • Trofimov V. I. On the action of a group on a graph // Acta Appl. Math., 1992, 29, 161–170.
  • Trofimov V. I. Kernels of van den Dries–Wilkie homomorphisms and $o$-automorphisms of graphs // J. Algebra, 2000, 226, 967–976.

https://www.mathnet.ru/eng/person8884
List of publications on Google Scholar
https://mathscinet.ams.org/mathscinet/MRAuthorID/193232

Publications in Math-Net.Ru Citations
2024
1. V. I. Trofimov, “On adjacency operators of locally finite graphs”, Izv. RAN. Ser. Mat., 88:3 (2024),  139–191  mathnet  mathscinet  zmath; Izv. Math., 88:3 (2024), 542–589  scopus
2023
2. V. I. Trofimov, “A Graph with a Locally Projective Vertex-Transitive Group of Automorphisms Aut($Fi_{22}$) Which Has a Nontrivial Stabilizer of a Ball of Radius $2$”, Trudy Inst. Mat. i Mekh. UrO RAN, 29:4 (2023),  274–278  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 323, suppl. 1 (2023), S300–S304  scopus
2022
3. V. I. Trofimov, “On the Weiss Conjecture. I”, Trudy Inst. Mat. i Mekh. UrO RAN, 28:1 (2022),  247–256  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 319, suppl. 1 (2022), S281–S290  isi  scopus
2019
4. V. I. Trofimov, “On Limits of Vertex-Symmetric Graphs and Their Automorphisms”, Trudy Inst. Mat. i Mekh. UrO RAN, 25:4 (2019),  226–234  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 309, suppl. 1 (2020), S167–S174  isi  scopus
2018
5. A. S. Kondrat'ev, V. I. Trofimov, “Stabilizers of vertices of graphs with primitive automorphism groups and a strong version of the Sims conjecture. IV”, Trudy Inst. Mat. i Mekh. UrO RAN, 24:3 (2018),  109–132  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 307, suppl. 1 (2019), S64–S87  isi 1
2017
6. N. Seifter, V. I. Trofimov, “Big subsets with small boundaries in a graph with a vertex-transitive group of automorphisms”, Izv. RAN. Ser. Mat., 81:1 (2017),  139–160  mathnet  mathscinet  zmath  elib; Izv. Math., 81:1 (2017), 137–155  isi  scopus
2016
7. A. S. Kondrat'ev, V. I. Trofimov, “Stabilizers of vertices of graphs with primitive automorphism groups and a strong version of the Sims conjecture. III”, Trudy Inst. Mat. i Mekh. UrO RAN, 22:4 (2016),  163–172  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 113–122  isi  scopus 3
8. A. S. Kondrat'ev, V. I. Trofimov, “Stabilizers of vertices of graphs with primitive automorphism groups and a strong version of the Sims conjecture. II”, Trudy Inst. Mat. i Mekh. UrO RAN, 22:2 (2016),  177–187  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 89–100  isi  scopus 4
2015
9. V. I. Trofimov, “The finiteness of the number of symmetrical extensions of a locally finite tree by a finite graph”, Trudy Inst. Mat. i Mekh. UrO RAN, 21:3 (2015),  303–308  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 168–173  isi 1
2014
10. E. A. Neganova, V. I. Trofimov, “Symmetrical extensions of graphs”, Izv. RAN. Ser. Mat., 78:4 (2014),  175–206  mathnet  mathscinet  zmath  elib; Izv. Math., 78:4 (2014), 809–835  isi  scopus 5
11. A. S. Kondrat'ev, V. I. Trofimov, “Stabilizers of vertices of graphs with primitive automorphism groups and a strong version of the Sims conjecture. I”, Trudy Inst. Mat. i Mekh. UrO RAN, 20:4 (2014),  143–152  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 146–155  isi  scopus 5
12. V. I. Trofimov, “Some remarks on symmetrical extensions of graphs”, Trudy Inst. Mat. i Mekh. UrO RAN, 20:2 (2014),  284–293  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 199–208  isi  scopus 3
2013
13. V. I. Trofimov, “The finiteness of the number of symmetrical 2-extensions of the $d$-dimensional lattice and similar graphs”, Trudy Inst. Mat. i Mekh. UrO RAN, 19:3 (2013),  290–303  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), S169–S182  isi  scopus 5
2012
14. V. I. Trofimov, “A note on the extendability of an isomorphism of subgraphs of a graph to an automorphism of the graph”, Trudy Inst. Mat. i Mekh. UrO RAN, 18:3 (2012),  26–29  mathnet  elib 1
2011
15. V. I. Trofimov, “Some topics in graph theory related with group theory”, Sib. Èlektron. Mat. Izv., 8 (2011),  62–67  mathnet 3
16. V. I. Trofimov, “Symmetrical extensions of graphs and some other topics in graph theory related with group theory”, Trudy Inst. Mat. i Mekh. UrO RAN, 17:4 (2011),  316–320  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 279, suppl. 1 (2012), 107–112  isi  scopus 5
17. E. A. Neganova, V. I. Trofimov, “On symmetrical $4$-extensions of the grid $\Lambda^2$”, Trudy Inst. Mat. i Mekh. UrO RAN, 17:3 (2011),  242–257  mathnet  elib 2
2010
18. E. A. Neganova, V. I. Trofimov, “On symmetrical $q$-extensions of the 2-dimensional grid”, Trudy Inst. Mat. i Mekh. UrO RAN, 16:3 (2010),  199–209  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S127–S137  isi  scopus 3
2007
19. V. I. Trofimov, “On the Fastest Moving Off from a Vertex in Directed Regular Graphs”, Mat. Zametki, 82:5 (2007),  770–782  mathnet  mathscinet  zmath  elib; Math. Notes, 82:5 (2007), 691–702  isi  scopus 1
2003
20. V. I. Trofimov, “Graphs with projective suborbits. Exceptional cases of characteristic 2. IV”, Izv. RAN. Ser. Mat., 67:6 (2003),  193–222  mathnet  mathscinet  zmath; Izv. Math., 67:6 (2003), 1267–1294  isi  scopus 8
2001
21. V. I. Trofimov, “Graphs with projective suborbits. Exceptional cases of characteristic 2. III”, Izv. RAN. Ser. Mat., 65:4 (2001),  151–190  mathnet  mathscinet  zmath; Izv. Math., 65:4 (2001), 787–822  scopus 9
22. V. I. Trofimov, “On a Property of Urysohn's Universal Metric Space”, Mat. Zametki, 69:2 (2001),  319–320  mathnet  mathscinet  zmath; Math. Notes, 69:2 (2001), 288–289  isi 1
2000
23. V. I. Trofimov, “Graphs with projective suborbits. Exceptional cases of characteristic 2. II”, Izv. RAN. Ser. Mat., 64:1 (2000),  175–196  mathnet  mathscinet  zmath; Izv. Math., 64:1 (2000), 173–192  isi  scopus 9
1998
24. V. I. Trofimov, “Graphs with projective suborbits. Exceptional cases of characteristic 2. I”, Izv. RAN. Ser. Mat., 62:6 (1998),  159–222  mathnet  mathscinet  zmath; Izv. Math., 62:6 (1998), 1221–1279  isi  scopus 14
1994
25. V. I. Trofimov, “Graphs with projective suborbits. Cases of small characteristics. II”, Izv. RAN. Ser. Mat., 58:6 (1994),  137–156  mathnet  mathscinet  zmath; Russian Acad. Sci. Izv. Math., 45:3 (1995), 559–576  isi 12
26. V. I. Trofimov, “Graphs with projective suborbits. Cases of small characteristics. I”, Izv. RAN. Ser. Mat., 58:5 (1994),  124–171  mathnet  mathscinet  zmath; Russian Acad. Sci. Izv. Math., 45:2 (1995), 353–398  isi 12
1991
27. V. I. Trofimov, “Graphs with projective suborbits”, Izv. Akad. Nauk SSSR Ser. Mat., 55:4 (1991),  890–916  mathnet  mathscinet  zmath; Math. USSR-Izv., 39:1 (1992), 869–893  isi 13
1990
28. V. I. Trofimov, “Vertex stabilizers of graphs with projective suborbits”, Dokl. Akad. Nauk SSSR, 315:3 (1990),  544–546  mathnet  mathscinet  zmath; Dokl. Math., 42:3 (1991), 825–828 6
1989
29. V. I. Trofimov, “On the action of primitive groups”, Algebra Logika, 28:3 (1989),  337–363  mathnet  mathscinet 4
30. V. I. Trofimov, “Certain asymptotic characteristics of groups”, Mat. Zametki, 46:6 (1989),  85–93  mathnet  mathscinet  zmath; Math. Notes, 46:6 (1989), 945–951  isi 3
1988
31. V. I. Trofimov, “The effect of the structure of a graph on the behavior of its automorphisms”, Algebra Logika, 27:2 (1988),  221–241  mathnet  mathscinet 2
1987
32. V. I. Trofimov, “Asymptotic behavior of automorphisms of graphs”, Mat. Sb. (N.S.), 134(176):2(10) (1987),  274–284  mathnet  mathscinet  zmath; Math. USSR-Sb., 62:1 (1989), 277–287 2
1986
33. V. I. Trofimov, “The action of a group on a graph”, Izv. Akad. Nauk SSSR Ser. Mat., 50:5 (1986),  1077–1096  mathnet  mathscinet  zmath; Math. USSR-Izv., 29:2 (1987), 429–447 5
1985
34. V. I. Trofimov, “Automorphism groups of graphs as topological groups”, Mat. Zametki, 38:3 (1985),  378–385  mathnet  mathscinet  zmath; Math. Notes, 38:3 (1985), 717–720  isi 36
1984
35. V. I. Trofimov, “Growth functions of permutation groups”, Trudy Inst. Mat. Sib. Otd. AN SSSR, 4 (1984),  118–138  mathnet  mathscinet  zmath
36. V. I. Trofimov, “Graphs with polynomial growth”, Mat. Sb. (N.S.), 123(165):3 (1984),  407–421  mathnet  mathscinet  zmath; Math. USSR-Sb., 51:2 (1985), 405–417 58
1983
37. V. I. Trofimov, “Automorphisms of graphs and a characterization of lattices”, Izv. Akad. Nauk SSSR Ser. Mat., 47:2 (1983),  407–420  mathnet  mathscinet  zmath; Math. USSR-Izv., 22:2 (1984), 379–391 23
1982
38. V. I. Trofimov, “Transitive permutation groups with a solvable one-point stabilizer”, Mat. Zametki, 32:3 (1982),  277–284  mathnet  mathscinet  zmath; Math. Notes, 32:3 (1982), 618–622  isi
1995
39. V. I. Trofimov, “Letter to the editor”, Izv. RAN. Ser. Mat., 59:4 (1995),  221  mathnet  mathscinet 2

Presentations in Math-Net.Ru
1. Eigenvalues and eigenfunctions of locally finite graphs
V. I. Trofimov
Iskovskikh Seminar
October 24, 2024 18:00   

Organisations
 
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