1.

Algorithmic Investigations in Combinatorics [in Russian], Nauka, Moscow (1978).

2.

V. L. Arlazarov, I. I. Zuev, A. V. Uskov, and I. A. Faradzhev, “Algorithms for bringing finite undirected graphs to canonic form,” Zh. Vychisl. Mat. Mat. Fiz.,

14, No. 3, 737–743 (1974).

Google Scholar3.

A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Algorithms, Addition-Wesley, Reading, MA (1974).

Google Scholar4.

B. Yu. Veisfeiler and A. A. Leman, “Reducing a graph to canonic form and the algebra arising here,” Nauchn.-Tekh. Inf., Ser. 2, No. 9, 12–16 (1968).

Google Scholar5.

G. G. Vizing, “Reduction of the problems of isomorphism and of the isomorphic imbedding of graphs to the problem of finding the incompleteness of a graph,” All-Union Conf. Cybernetics Problems [in Russian], Novosibirsk (1974), pp. 124–125.

6.

D. Yu. Grigor'ev, “The reduction of graph isomorphism to polynomial problems,” J. Sov. Math.,

20, No. 4, 2296–2298 (1982).

Google Scholar7.

D. Yu. Grigor'ev, “Complexity of ‘wild’ matrix problems and of the isomorphism of algebras and graphs,” J. Sov. Math.,

22, No. 3 1285–1289 (1983).

Google Scholar8.

M. A. Zaitsev, “On the 3-edge isomorphism of graphs,” Vopr. Kibernet., No. 26, 65–76 (1978).

Google Scholar9.

M. A. Zaitsev, “On the Hamiltonian isomorphism of graphs,” Mat. Zametki,

25, No. 2, 299–306 (1979).

Google Scholar10.

V. N. Zemlyachenko, “Canonic enumeration of trees,” Proc. Sem. Combinatorial Analysis [in Russian], Moscow State Univ. (1970).

11.

V. N. Zemlyachenko, “On graph identification algorithms,” Vopr. Kibern., No. 15, 33–41 (1975).

Google Scholar12.

V. N. Zemlyachenko, “Establishment of graph isomorphism,” Mathematical Questions on Modeling Complex Objects [in Russian], Petrozavodsk (1979).

13.

V. N. Zemlyachenko, “Polynomial identification algorithms of almost all graphs,” Mathematical Questions on Modeling Complex Objects, Petrozavodsk (1982).

14.

R. M. Karp, “Reducibility of combinatorial problems,” in: Complexity of Computer Computations, IBM Research Center, Yorktown Heights, NY (1972).

Google Scholar15.

N. M. Korneenko, “Properties of metric spaces of graph isomorphism classes,” Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk, No. 2, 32–36 (1981).

Google Scholar16.

N. M. Korneenko, “On the complexity of computation of the distance between graphs,” Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk, No. 1 (1982).

17.

A. I. Kostyukovich, “Polynomial equivalence of certain discrete optimization problems,” Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk, No. 4, 47–49 (1979).

Google Scholar18.

S. A. Cook, “The complexity of theorem-proving procedures,” Proc. Third Ann. ACM Sympos. Theory of Computing, Assoc. Comput. Mach., New York (1971), pp. 151–158.

Google Scholar19.

V. K. Leont'ev, “Local optimization algorithm for solving certain combinatorial problems,” Vopr. Kibern., No. 15, 61–66 (1975).

Google Scholar20.

N. N. Metel'skii and N. M. Korneenko, “Metrization of one class of graphs,” Dokl. Akad. Nauk BSSR,

23, No. 1, 5–7 (1979).

Google Scholar21.

A. A. Mironov, “Some properties of number sets realizable in graphs,” Tr. Mosk. Inst. Inzh. Transport., No. 640, 115–120 (1979).

Google Scholar22.

O. Ore, Theory of Graphs, Am. Math. Soc., Providence, RI (1962).

Google Scholar23.

C. C. Sims, “Computational methods in the study of permutation groups,” in: Computational Problems in Abstract Algebra, Pergamon Press, Oxford (1970), pp. 169–183.

Google Scholar24.

D. A. Suprunenko, Groups of Matrices [in Russian], Nauka, Moscow (1972).

Google Scholar25.

S. A. Trakhtenbrot, “On the theory of repetition-free contact schemes,” Tr. Mat. Inst. Steklov. Akad. Nauk SSSR,

51, 226–269 (1958).

Google Scholar26.

R. I. Tyshkevich, “Canonic decomposition of a graph,” Dokl. Akad. Nauk BSSR,

24, No. 8, 677–679 (1980).

Google Scholar27.

F. Harary, Graph Theory, Addison-Wesley, Reading, MA (1969).

Google Scholar28.

M. Hall, Jr., The Theory of Groups, MacMillan, New York (1959).

Google Scholar29.

J. E. Hopcroft and R. E. Tarjan, “Isomorphism of planar graphs,” in: Complexity of Computer Computations, IBM Research Center, Yorktown Heights, NY (1972).

Google Scholar30.

D. Angluin, “On counting problems and the polynomial hierarchy,” Theor. Comput. Sci.,

12, No. 2, 161–163 (1980).

Google Scholar31.

M. D. Atkinson, “An algorithm for finding the blocks of a permutation group,” Math. Comput.,29, No. 131 (1975).

32.

L. Babai, “On the isomorphism problem,” App. to Proc. Conf. Foundat. Comput. Theory, Poland (1977), pp. 19–23.

33.

L. Babai, “The star-system problem is at least as hard as the graph isomorphism problem,” in: A. Hajnal and V. T. Sós (eds.), Combinatorics, Vol. II, North-Holland, Amsterdam-Oxford-New York (1978), p. 1214.

Google Scholar34.

L. Babai, “Monte-Carlo algorithms in graph isomorphism testing,” Preprint, Univ, Toronto (1979).

35.

L. Babai, “Isomorphism testing and symmetry of graphis,” Ann. Discrete Math.,

8, 101–109 (1980).

Google Scholar36.

L. Babai, “On the complexity of canonical labeling of strongly regular graphs,” SIAM J. Comput.,

9, 212–216 (1980).

Google Scholar37.

L. Babai, “Moderately exponential bound for graph isomorphism,” in: Fundamentals of Computation Theory, F. Gecseg (ed.), Lect. Notes Comput. Sci., Vol. 117, Springer-Verlag, Berlin-Heidelberg-New York (1981), pp. 34–50.

Google Scholar38.

L. Babai, P. J. Cameron, and P. P. Pàlfy, “On the order of primitive permutation groups with bounded non-Abelian composition factors,” Preprint (1981).

39.

L. Babai and P. Erdös, “Random graph isomorphism,” Preprint (1977).

40.

L. Babai, P. Erdös, and S. M. Selkow, “Random graph isomorphism,” SIAM J. Comput.,

9, No. 3, 628–635 (1980).

Google Scholar41.

L. Babai and L. Kucera, “Canonical labeling of graphs in linear average time,” 20th Ann. Sympos. Foundations Comput. Sci., IEEE Computer Soc., New York (1979), pp. 39–46.

Google Scholar42.

L. Babai and L. Lovász, “Permutation groups and almost regular graphs,” Stud. Sci. Math. Hungar.,

8, 141–150 (1973).

Google Scholar43.

M. Behzad, “The degree preserving group of a graph,” Riv. Mat. Univ. Parma, No. 11, 307–311 (1970).

Google Scholar44.

K. S. Booth, “Isomorphism testing for graphs, semigroups and finite automata are polynomially equivalent problems,” SIAM J. Comput.,

7, No. 3, 273–279 (1978).

Google Scholar45.

K. S. Booth, “Problems polynomially equivalent to graph isomorphism,” Proc. Sympos. New Directions and Recent Results in Algorithms and Complexity, Carnegie-Mellon Univ. (1979).

46.

C. J. Colburn, “On testing isomorphism of permutation graphs,” Networks,

11, No. 1, 13–21 (1981).

Google Scholar47.

M. J. Colburn and C. J. Colburn, “Graph isomorphsim and self-complementary graphs,” SIGACT News,

10, No. 1, 25–29 (1978).

Google Scholar48.

M. J. Colburn and C. J. Colburn, “The complexity of combinatorial isomorphism problems, Ann. Discrete Math.,

8, 113–116 (1980).

Google Scholar49.

C. J. Colburn and D. G. Corneil, “On deciding switching equivalence of graphs,” Discrete Appl. Math.,

2, 181–184 (1980).

Google Scholar50.

C. J. Colburn, “The complexity of symmetrizing matrices,” Inf. Process. Lett.,

9, No. 3, 108–109 (1979).

Google Scholar51.

D. G. Corneil, “Recent results on the graph isomorphism problem,” in: Proc. Eighth Manitoba Conf. Numer. Math. and Computing, D. McCarthy and H. C. Williams (eds.), Utilitas Mathematica Publ., Inc., Winnipeg, Man. (1979), pp. 13–31.

Google Scholar52.

D. G. Cornell and C. C. Gotlieb, “An efficient algorithm for graph isomorphism,” J. Assoc. Comput. Mach.,

17, 51–64 (1970).

Google Scholar53.

D. G. Corneil and D. G. Kirkpatrick, “A theoretical analysis of various heuristics for the graph isomorphism problem,” SIAM J. Comput.,

9, No. 2, 281–297 (1980).

Google Scholar54.

N. Deo, J. M. Davis, and R. E. Lord, “A new algorithm for diagraph isomorphism,” BIT,

17, 16–30 (1977).

Google Scholar55.

P. Erdös and A. Renyi, “Asymmetric graphs,” Acta Math. Acad. Sci. Hung.,

14, 295–315 (1963).

Google Scholar56.

R. A. Edmonds, “A combinatorial representation for polyhedral surfaces,” Not. Am. Math. Soc.,

7, 646 (1960).

Google Scholar57.

I. S. Filotti and J. N. Mayer, “A polynomial-time algorithm for determining the isomorphism of graphs of fixed genus,” Conf. Proc. Twelfth Ann. ACM Sympos. Theory of Computing, Assoc. Comput. Mach., New York (1980), pp. 236–243.

Google Scholar58.

I. S. Filotti, G. L. Miller, and J. Reif, “On determining the genus of a graph in O(v

^{O(g)}) steps,” Conf. Record Eleventh Ann. ACM Sympos. Theory of Comput., Assoc. Comput. Mach., New York (1979), pp. 27–37.

Google Scholar59.

R. Frucht, “Herstellung von Graphen mit vorgebener abstrakter Gruppe,” Compositio Math.,

6, 239–250 (1938).

Google Scholar60.

R. Frucht, “Lattice with a given abstract group,” Can. J. Math.,

2, 417–419 (1950).

Google Scholar61.

M. Furst, J. Hopcroft, and E. Luks, “A subexponential algorithm for trivalent graph isomorphism,” Congr. Numer.,

28, 421–446 (1980).

Google Scholar62.

M. Furst, J. Hopcroft, and E. Luks, “Polynomial-time algorithms for permutation groups,” 21st Ann. Sympos. Foundations Comput. Sci., IEEE, NY (1980), pp. 36–41.

Google Scholar63.

M. R. Garey and D. S. Johnson, Computers and Intractability, W. H. Freeman, San Francisco (1979).

Google Scholar64.

G. Gati, “Further annotated bibliography on the isomorphism disease,” J. Graph Theory,

3, No. 2, 95–104 (1979).

Google Scholar65.

M. K. Goldberg, “A nonfactorial algorithm for testing isomorphism of two graphs,” Combinatorics and Optimization, Research Reports, No. 80-36, Faculty Math. Univ. Waterloo (1980).

66.

D. Gries, “Describing an algorithm by Hopcroft,” Acta Inf.,

2, 97–109 (1973).

Google Scholar67.

R. Halin and H. A. Young, “A note on isomorphism of graphs,” J. London Math. Soc.,

42, No. 2, 254–256 (1967).

Google Scholar68.

Z. Hedrlin and A. Pultr, “On the full embeddings of categories of algebras,” Ill. J. Math.,

10, 392–406 (1966).

Google Scholar69.

P. Hell and J. Nesetril, “Graphs and k-societies,” Can. Math. Bull.,

13, No. 3, 375–381 (1970).

Google Scholar70.

D. G. Higman, “Coherent configurations. I,” Geometriae Dedicata,

4, 1–32 (1975).

Google Scholar71.

J. E. Hopcroft, An n log n algorithm for isomorphism of planar triplet connected graphs,” Stanford Comput. Sci. Rept., STAN-CS-71-192 (1971).

72.

J. Hopcroft, “An n log n algorithm for minimizing states in a finite automaton,” in: Theory of Machines and Computations, Z. Kohavi and A. Paz (eds.), Academic Press, New York-London (1971), pp. 189–196.

Google Scholar73.

J. E. Hopcroft and R. E. Tarjan, “Dividing a graph into triconnected components,” SIAM J. Comput.,

2, No. 3, 136–158 (1973).

Google Scholar74.

J. E. Hopcroft and R. E. Tarjan, “Efficient planarity testing,” J. Assoc. Comput. Mach.,

21, No. 4, 549–568 (1974).

Google Scholar75.

J. E. Hopcroft and J. K. Wong, “Linear time algorithm for isomorphism of planar graphs; preliminary report,” Sixth Ann. ACM Sympos. Theory Comput., Assoc. Comput. Mach., New York (1974), pp. 172–184.

Google Scholar76.

H. B. Hunt, III and D. J. Rosenkrantz, “Complexity of grammatical similarity relations,” Proc. Conf. Theor. Comput. Sci., Comput. Sci. Dept., Univ. Waterloo, Ontario (1978), pp. 139–145.

Google Scholar77.

R. M. Karp, “Probabilistic analysis of a canonical labeling algorithm for graphs,” Proc. Sympos. Pure Math., Vol. 34, Am. Math. Soc., Providence, RI (1979), pp. 365–378.

Google Scholar78.

D. Kozen, “Complexity of finitely presented algebras,” Conf. Record Ninth Ann. ACM Sympos. Theory of Comput., Assoc. Comput. Mach., New York (1977), pp. 164–167.

Google Scholar79.

D. Kozen, “A clique problem equivalent to graph isomorphism,” SIGACT News,

10, No. 2, 50–52 (1978).

Google Scholar80.

L. Kucera, “Theory of categories and negative results in computational complexity,” Preprint, Karlov Univ., Prague (1976).

Google Scholar81.

F. Lalonde, “Le problème d'étoiles pour graphes est NP-complet,” Discrete Math.,

33, No. 3, 271–280 (1981).

Google Scholar82.

L. Lesniak-Foster, “Parameter-preserving group of a graph,” Riv. Mat. Univ. Parma, No. 1, 113–117 (1975 (1977)).

Google Scholar83.

G. Levi, “Graph isomorphism: A heuristic edge-partitioning-oriented algorithm,” Computing,

12, 291–313 (1977).

Google Scholar84.

D. Lichtenstein, “Isomorphism for graphs embeddable on the projective plane,” Conf. Proc. Twelfth Ann. ACM Sympos. Theory Comput., Assoc. Comput. Mach., New York (1980), pp. 218–224.

Google Scholar85.

R. M. Lipton, “The beacon set approach to graph isomorphism,” SIAM J. Comput.,9 (1980).

86.

L. Lovasz, “On the ratio of optimal and fractional cover,” Discrete Math.,

13, 383–390 (1975).

Google Scholar87.

A. Lubiw, “Some NP-complete problems similar to graph isomorphism,” SIAM J. Comput.,

10, No. 1, 11–21 (1981).

Google Scholar88.

G. S. Lueker and K. S. Booth, “A linear time algorithm for deciding interval graph isomorphism,” J. Assoc. Comput. Mach.,

26, No. 2, 183–195 (1979).

Google Scholar89.

E. M. Luks, “Isomorphism of graphs of bounded valence can be tested in polynomial time,” 21st Ann. Sympos. Foundations Comput. Sci., IEEE, Inc., New York (1980), pp. 42–49.

Google Scholar90.

R. Mathon, “Sample graphs for isomorphism testing,” in: Proc. Ninth S. E. Conf. Combinatorics, Graph Theory, Comput., F. Hoffman, D. McCarthy, R. C. Mullin, and R. G. Stanton (eds.), Utilitas Mathematica Publ. Inc., Winnipeg, Man. (1978), pp. 499–517.

Google Scholar91.

R. Mathon, “A note on graph isomorphism counting problems,” Inf. Process. Lett.,

8, No. 3, 131–132 (1978).

Google Scholar92.

B. D. McKay, “Computing algorithms and canonical labeling of graphs,” in: Combinatorial Mathematics, Lect. Notes Math., Vol. 686, Springer-Verlag, Berlin-Heidelberg-New York (1978), pp. 223–232.

Google Scholar93.

B. D. McKay, “Backtrack programming and isomorph rejection on ordered subsets,” Ars Combin.,

5, 65–69 (1978).

Google Scholar94.

B. D. McKay, “Hadamard equivalence via graph isomorphism,” Discrete Math.,

27, No. 2, 213–214 (1979).

Google Scholar95.

C. J. Colburn and B. D. McKay, “A dorrection to Colburn's paper on the complexity of matrix symmetrizability,” Inf. Process. Lett.,

11, No. 2, 96–97. (See [50].)(.

Google Scholar96.

G. L. Miller, “Graph isomorphism, general remarks,” Conf. Record Ninth Ann. ACM Sympos. Theory Comput., Assoc. Comput. Mach., New York (1977), pp. 143–150.

Google Scholar97.

G. L. Miller, “On the n

^{log n} isomorphism technique (a preliminary report),” Conf. Record Tenth Ann. ACM Sympos. Theory Comput., Assoc. Comput. Mach., New York (1978), pp. 51–58.

Google Scholar98.

G. L. Miller, “Graph isomorphism, general remarks,” J. Comput. Syst. Sci.,

18, 128–142 (1979).

Google Scholar99.

G. L. Miller, “Isomorphism testing for graphs of bounded genus,” Conf. Proc. Twelfth Ann. ACM Sympos. Theory Comput., Assoc. Comput. Mach., New York (1980), pp. 225–235.

Google Scholar100.

A. Pultr, “Concerning universal categories,” Comment. Math. Univ. Carolinae,

5, 227–239 (1964).

Google Scholar101.

R. C. Read and D. G. Corneil, “The graph isomorphism disease,” J. Graph Theory,

1, 339–363 (1977).

Google Scholar102.

F. Schweiggert, “Zur isomorphie endlicher Graphen und Strukturen,” Diss. Dok. Naturwiss. (1979).

103.

F. Sirovich, “Isomorfismo fra grafi: un algoritmo efficiente per trovare tutti gli isomorphismi,” Calcolo,

8, No. 4, 301–337 (1971).

Google Scholar104.

V. T. Sós, in: The Problems section of: A. Hajnal and V. T. Sós (eds.), Combinatorics, Vol. II, North-Holland, Amsterdam-Oxford-New York (1978), p. 1214. (See [33].)

Google Scholar105.

J. Turner, “Generalized matrix functions and the graph isomorphism problem,” SIAM J. Appl. Math.,

16, No. 3, 520–526 (1968).

Google Scholar106.

S. H. Unger, “GIT: a heuristic program for testing pairs of directed line graphs for isomorphism,” Commun. Assoc. Comput. Mach.,

7, No. 1, 26–34 (1964).

Google Scholar107.

L. G. Valiant, “The complexity of computing the permanent,” Theor. Comput. Sci.,

8, 189–201 (1979).

Google Scholar108.

H. De Vries and A. B. De Miranda, “Groups with small number of automorphisms,” Math. Z.,

68, 450–464 (1958).

Google Scholar109.

L. Weinberg, “Plane representations and codes for planar graphs,” Proc. Third Ann. Allerton Conf. Circuit Syst. Theory (1965), pp. 733–744.

110.

L. Weinberg, “A simple and efficient algorithn for determining isomorphism of planar triply connected graphs,” IEEE Trans. Commun. Technol.,

CT-13, 142–148 (1960).

Google Scholar111.

B. Weisfeiler, “On construction and identification of graphs,” Lect. Notes Math.,

558, Springer-Verlag, Berlin-Heidelberg-New York (1976).

Google Scholar112.

H. Whitney, “Congruent graphs and the connectivity of graphs,” Am. J. Math.,

54, 150–168 (1932).

Google Scholar113.

H. Whitney, “A set of topological invariants for graphs,” Am. J. Math.,

55, 221–235 (1933).

Google Scholar114.

H. Whitney, “On the classification of graphs,” Am. J. Math.,

55, 236–244 (1933).

Google Scholar115.

H. Whitney, “2-isomorphic graphs,” Am. J. Math.,

55, 245–254 (1933).

Google Scholar116.

F. F. Yao, “Graph 2-isomorphism is NP-complete,” Inf. Process. Lett.,

9, No. 2, 68–72 (1979).

Google Scholar117.

B. Zelinka, “On a certain distance between isomorphism classes of graphs,” Casopis Pest. Math.,100, No. 4, 371–373.