01.01.09 (Discrete mathematics and mathematical cybernetics)
E-mail:
,
Keywords:
graphs, diameter, diametral vertices, central vertices, center, almost all graphs, typical graphs, metric ball and sphere, number of balls, diversity vector of balls
UDC:
519.1, 519.17, 519.7, 519.173, 519.176, 519.178
Subject:
graphs, metric properties of graphs,
typical graphs, typical properties of graphs, combinatorics, combinatorial analysis
Main publications:
T. I. Fedoryaeva, “Center and its spectrum of almost all n-vertex graphs of given diameter”, Siberian Electronic Mathematical Reports, 2021, 511-529
T. I. Fedoryaeva, “Asymptotic approximation for the number of n-vertex graphs of given diameter”, Journal of Applied and Industrial Mathematics, 11:2 (2017), 204-211
T. I. Fedoryaeva, “Structure of the diversity vector of balls of a typical graph with given diameter”, Sib. Electr. Math. Reports, 13 (2016), 375–387.
T. I. Fedoryaeva, “Majorants and minorants for the classes of graphs with fixed diameter and number of vertices”, Journal of Applied and Industrial Mathematics, 7:2 (2013), 153-165
T. I. Fedoryaeva, "Combinatorial algorithms", Novosibirsk, 2011, ISBN: 978-5-4437-0019-9 , 118 pp.
T. I. Fedoryaeva, “Exact upper estimates of the number of different balls of given radius for the graphs with fixed number of vertexes and diameter”, Diskret. Analysis and Oper. Reseach, 16:6 (2009), 74–92.
T. I. Fedoryaeva, “Diversity vectors of balls in graphs and estimates of the components of the vectors”, Journal of Applied and Industrial Mathematics, 2:3 (2008), 341–356.
T. I. Fedoryaeva, “Variety of balls in metric spaces of trees”, Diskret. Analysis and Oper. Reseach, 12:3 (2005), 74–84.
T. I. Fedoryaeva, “Outerplanar graphs with the metric continuation property. I, II”, Diskret. Analysis and Oper. Reseach, 7:1 (2000), 83–112; Diskret. Analysis and Oper. Reseach, 8:1 (2001), 88–112.
T. I. Fedoryaeva, “On binomial coefficients of real arguments”, Siberian Electronic Mathematical Reports, 20:1 (2023), 514–523
2.
T. I. Fedoryaeva, “On Binomial coefficients of real arguments”, 2022 (Published online) , arXiv: 2206.03007
3.
T.I.Fedoryaeva, “Tipichnye metricheskie svoistva n-vershinnykh grafov zadannogo diametra”, “Diskretnaya matematika i ee prilozheniya”, Materialy XIV Mezhdunarodnogo seminara “Diskretnaya matematika i ee prilozheniya” imeni akademika O.B. Lupanova (Moskva, MGU, 20–25 iyunya 2022g.), Pod redaktsiei V.V. Kochergina, IPM im. Keldysha, Moskva, 2022, 21–33
4.
T. I. Fedoryaeva, “Logarithmic asymptotics of the number of central vertices of almost all n-vertex graphs of diameter k”, Siberian Electronic Mathematical Reports, 19:2 (2022), 747–761
T.I. Fedoryaeva, “Classification of graphs of diameter 2”, Conference “Women in Mathematics” (Novosibirsk, Russia, May 12, 2021), Sobolev Institute of Mathematics, Novosibirsk State University and Mathematical Center in Akademgorodok, Novosibirsk, 2021 http://math.nsc.ru/LBRT/d5/conference/WM/2021/Talks/T_Fedoryaeva.pdf
9.
T.I. Fedoryaeva, “Radius of almost all n-vertex graphs of given diameter”, Materialy XIX mezhdunarodnoi konferentsii “Problemy teoreticheskoi kibernetiki”. (Kazan, Rossiya, 28 Sentyabrya - 01 Oktyabrya, 2021), Kazanskii federalnyi universitet, Kazan, 2021, 132-135
10.
T. I. Fedoryaeva, “Classification of graphs of diameter 2”, Siberian Electronic Mathematical Reports, 2020, 502–512
11.
T.I. Fedoryaeva, “Graphs of diameter 2 and their diametral vertices”, Proceedings of the International Conference “2020 Ural Workshop on Group Theory and Combinatorics”. (Yekaterinburg, Russia, August 24-30, 2020), Institute of Natural Sciences and Mathematics of Ural Federal University, Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, The Ural Mathematical Center, Yekaterinburg, 2020, P.41
12.
A. A. Evdokimov, T. I. Fedoryaeva, “Tree-like structure graphs with full diversity of balls”, J. Appl. Industr. Math., 12:1 (2018), 19-27
13.
A. A. Evdokimov, T. I. Fedoryaeva, “Tree-like structure graphs with full diversity of balls”, J. Appl. Industr. Math., 12:1 (2018), 19-27
14.
T. I. Fedoryaeva, “Asymptotic approximation for the number of n-vertex graphs of given diameter”, J. Appl. Industr. Math., 11:2 (2017), 204-214
15.
T.I.Fedoryaeva, “Vektor raznoobraziya sharov tipichnogo grafa zadannogo diametra”, Matematika v sovremennom mire. Tezisy dokladov Mezhdunarodnoi konferentsii, posvyaschennoi 60-letiyu Instituta matematiki im. S.L.Soboleva (Novosibirsk, 14–19 avgusta 2017 g.), Izdatelstvo Instituta matematiki, 2017, 457http://math.nsc.ru/conference/mmw/2017/Book_Abstract.pdf
16.
T. I. Fedoryaeva, “Asymptotic approximation for the number of n-vertex graphs of given diameter”, J. Appl. Industr. Math., 11:2 (2017), 204-214
T. I. Fedoryaeva, “Structure of the diversity vector of balls of a typical graph with given diameter”, Sib. Èlektron. Mat. Izv., 13 (2016), 375–387
18.
T. I. Fedoryaeva, “Computing the diversity vectors of balls of a given graph”, Sib. Èlektron. Mat. Izv., 13 (2016), 122–129
19.
T.I. Fedoryaeva, “Asymptotic approximation for the number of n-vertex graphs with given diameter”, Proceedings of the International Conference and PhD-Master Summer School on Graphs and Groups, Spectra and Symmetries. (Novosibirsk: Sobolev Institute of Mathematics), Sobolev Institute of Mathematics & Novosibirsk State University, Novosibirsk, 2016, P.55
T. I. Fedoryaeva, “On the diversity of balls in a typical graph of a given diameter”, Prikl. Diskr. Mat. Suppl., 2015, no. 8, 127–128
22.
T. I. Fedoryaeva, “The diversity vector of balls of a typical graph of small diameter”, Diskretn. Anal. Issled. Oper., 22:6 (2015), 43–54
23.
A. A. Evdokimov, T. I. Fedoryaeva, “On the problem of characterizing the diversity vectors of balls”, J. Appl. Industr. Math., 8:2 (2014), 190–195
24.
A. A. Evdokimov, T. I. Fedoryaeva, “On the problem of characterizing the diversity vectors of balls”, Journal of Applied and Industrial Mathematics, 8:2 (2014), 190-195
25.
Fedoryaeva T.I. (sovmestno s Evdokimovym A.A.), “O graficheskom raznoobrazii sharov”, Problemy teoreticheskoi kibernetiki, materialy XVII mezhdunarodnoi konferentsii (Kazan, 2014), Otechestvo, Kazan, 2014, 77-80http://elibrary.ru/item.asp?id=23739366
26.
T. I. Fedoryaeva, “Majorants and minorants in the graph class with given number of vertices and diameter”, J. Appl. Industr. Math., 7:2 (2013), 153–165
27.
T. I. Fedoryaeva, “Mazhoranty i minoranty klassa n-vershinnykh grafov diametra d”, Materialy mezhdunarodnoi konferentsii “Diskret. optimizatsiya i issled. operatsii” (Novosibirsk, 24–28 iyunya 2013 g.), Izdatelstvo Instituta matematiki, Novosibirsk, 2013, 114http://math.nsc.ru/conference/door/2013/Book
28.
T. I. Fedoryaeva, “Majorants and minorants for the classes of graphs with fixed diameter and number of vertices”, Journal of Applied and Industrial Mathematics, 7:2 (2013), 153-165
29.
T. I. Fedoryaeva, “Raznoobrazie sharov v grafakh s fiksirovannymi chislom vershin i diametrom”, Problemy teoreticheskoi kibernetiki, Izdatelstvo Nizhegorodskogo gosuniversiteta, Nizhnii Novgorod, 2011, 491–495
30.
T. I. Fedoryaeva, “On the graphs with given diameter, number of vertices, and local diversity of balls”, Journal of Applied and Industrial Mathematics, 5:1 (2011), 44–50
T. I. Fedoryaeva, “On graphs with given diameter, number of vertices, and local diversity of balls”, J. Appl. Industr. Math., 5:1 (2011), 44–50
32.
T. I. Fedoryaeva, “Exact upper estimates of the number of different balls of given radius for the graphs with fixed number of vertexes and diameter”, Diskretn. Anal. Issled. Oper., 16:6 (2009), 74–92
33.
T. I. Fedoryaeva, “Tochnye verkhnie otsenki komponent vektorov raznoobraziya sharov dlya grafov s zadannymi chislom vershin i diametrom”, Materialy XVII Mezhdunar. shkoly-seminara “Sintez i slozhnost upravlyayuschikh sistem” im. akademika O.B.Lupanova., Izdatelstvo Instituta matematiki, Novosibirsk, 2008, 167–172
34.
T. I. Fedoryaeva, “Diversity vectors of balls in graphs and estimates of the components of the vectors”, Journal of Applied and Industrial Mathematics, 2:3 (2008), 341–356
35.
T. I. Fedoryaeva, J. Appl. Industr. Math., 2:3 (2008), 341–356
36.
T. I. Fedoryaeva, “Vektory raznoobraziya sharov i svoistva ikh komponent”, Trudy VII Mezhdunarodnoi konferentsii “Diskretnye modeli v teorii upravlyayuschikh sistem”, MGU, Moskva, 2006, 374-378
37.
T. I. Fedoryaeva, “Variety of balls in metric spaces of trees”, Diskretn. Anal. Issled. Oper., 12:3 (2005), 74–84
38.
T. I. Fedoryaeva, “O raznoobrazii metricheskikh sharov v grafakh”, Problemy teoreticheskoi kibernetiki, Tezisy dokladov XIV Mezhdunarodnoi konferentsii (Penza, 23–28 maya 2005 g.), Izd-vo mekh.-mat. fak-ta MGU, Moskva, 2005, 158http://new.math.msu.su/department/dm/dmmc/CONF/14k_tez.pdf
39.
T. I. Fedoryaeva, “The property of metric continuation of the shortest paths in graphs”, Diskretn. Anal. Issled. Oper., 11:4 (2004), 56–67
40.
T. I. Fedoryaeva, “Grafy, imeyuschie prodolzhenie kratchaishikh tsepei”, Materialy XV Mezhdunar. shkoly-seminara “Sintez i slozhnost upravlyayuschikh sistem” (Moskva, 18–23 oktyabrya 2004 g.), Izd-vo mekh.-mat. fak-ta MGU, Moskva, 2004, 105–109
41.
T. I. Fedoryaeva, “Svoistvo metricheskogo prodolzheniya kratchaishikh tsepei”, Materialy konferentsii “Diskret. analiz i issled. operatsii” (Novosibirsk, 28 iyunya-2 iyulya 2004 g.), Izdatelstvo Instituta matematiki, Novosibirsk, 2004, 81
42.
T. I. Fedoryaeva, “Outerplanar graphs with the metric continuity property. II”, Diskretn. Anal. Issled. Oper., 8:1 (2001), 88–112
43.
T. I. Fedoryaeva, “Outerplanar graphs with the metric continuation property. I”, Diskretn. Anal. Issled. Oper., 7:1 (2000), 83–112
44.
T. I. Fedoryaeva, “Operations and Isometric Embeddings of Graphs Related to the Metric Prolongation Property”, Mathematics and Its Applications, 391, Operations Research and Discrete Analysis (1997), 31–49
45.
T. I. Fedoryaeva, “Izometricheskie vlozheniya grafov i operatsii grafov, svyazannye so svoistvom prodolzheniya metriki”, Materialy XI Mezhdunar. konf. po probl. teoret. kiber. (Ulyanovsk, 10–14 iyulya 1996 g.), Ros. gos. gumanit. un-t, Moskva, 1996, 196–197
46.
T. I. Fedoryaeva, “Svoistvo prodolzheniya metriki i porog otdelimosti otobrazhenii”, Materialy XI Mezhdunar. konf. po probl. teoret. kiber. (Ulyanovsk,, 10–14 iyulya 1996 g.), Ros. gos. gumanit. un-t, Moskva, 1996, 194–195
47.
T. I. Fedoryaeva, “Operatsii i izometricheskie vlozheniya grafov, svyazannye so svoistvom prodolzheniya metriki”, Diskretn. analiz i issled. oper., 2:3 (1995), 49–67
T. I. Fedoryaeva, “Kharakterizatsiya klassov grafov so svoistvom prodolzheniya metriki”, Metody i sistemy tekhnicheskoi diagnostiki, Materialy X Mezhdunar. konf. po probl. teoret. kib., 18, Izdatelstvo Saratovskogo gosuniversitete, Saratov, 1993, 175
49.
T. I. Fedoryaeva, “Usilennye svoistva prodolzheniya metriki”, Metody diskretnogo analiza v teorii grafov i slozhnosti, 1992, no. 52, 112–118
50.
T. I. Fedoryaeva, “Kharakterizatsiya odnogo klassa grafov so svoistvom prodolzheniya metriki”, Metody diskretnogo analiza v issledovanii funktsionalnykh sistem, 1988, no. 47, 89-93
51.
T. I. Fedoryaeva, D. M. Smirnov, “O reshetkakh kongruents-klassov regulyarnykh algebr”, Materialy XIX Vsesoyuzn. algebraicheskaya konf. (Lvov.), Lvov, 1987, 262
Books
52.
T. I. Fedoryaeva, Kombinatornye algoritmy, Izd-vo NGU, Novosibirsk, 2011 , 118 pp.
Thesis
53.
T. I. Fedoryaeva, Grafy, udovletvoryayuschie svoistvu prodolzheniya metriki, Avtoreferat Diss.kand. fiz.-matem. nauk, Institut matematiki SO RAN, Novosibirsk, 1996 , 12 pp.
54.
T. I. Fedoryaeva, Grafy, udovletvoryayuschie svoistvu prodolzheniya metriki, Diss. kand. fiz.-matem. nauk, Izdatelstvo Instituta matematiki, Novosibirsk, 1996 , 109 pp.
Proceedings
55.
T. I. Fedoryaeva, “Otsenki chisla razlichnykh sharov zadannogo radiusa v grafakh”, Matematika v sovremennom mire, Rossiiskaya konf., posvyaschennaya 50-letiyu IM SO RAN (Novosibirsk, 17–22 sentyabrya 2007 g.), Izdatelstvo Instituta matematiki, Novosibirsk, 2007, 290http://www.mathnet.ru/php/conference.phtml?confid=34&option_lang=rus
Preprints
56.
T. I. Fedoryaeva, Vneshneplanarnye grafy, udovletvoryayuschie svoistvu prodolzheniya metriki.I, Preprint № 1, Izdatelstvo Instituta matematiki, Novosibirsk, 1995 , 50 pp.
57.
T. I. Fedoryaeva, Vneshneplanarnye grafy, udovletvoryayuschie svoistvu prodolzheniya metriki.II, Preprint № 2, Izdatelstvo Instituta matematiki, Novosibirsk, 1995 , 28 pp.
58.
T. I. Fedoryaeva, Vneshneplanarnye grafy, udovletvoryayuschie svoistvu prodolzheniya metriki.III, Preprint № 3, Izdatelstvo Instituta matematiki, Novosibirsk, 1995 , 50 pp.
Popular science or education materials
59.
T. I. Fedoryaeva, Rabochaya programma distsipliny DISKRETNAYa MATEMATIKA, Novosibirskii gosudarstvennyi universitet, Novosibirsk, 2020 , 20 pp.
Information matherials
60.
A. A. Evdokimov, C. V. Avgustinovich, A. D. Korshunov, Yu. V. Merekin, V. V. Nyu, A. L. Perezhogin, T. I. Fedoryaeva, A. E. Frid, “Metricheskie i kombinatornye voprosy diskretnogo analiza”, Nir/Niokr, 1996.
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