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Partial geometries, their extensions, and related graphs

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References

  1. A. Blokhuis and A. Brouwer, “Locally 4-by-4 grid graphs,”J. Graph Theory,13, 229–244 (1989).

    Article  Google Scholar 

  2. A. E. Brouwer, A. Cohen, and A. Neumaier,Distance-Regular Graphs, Springer-Verlag (1989).

  3. A. Brouwer and M. Numata, “A characterization of some graphs which do not contain 3-claws,”Discr. Math.,124, 49–54 (1994).

    Article  MATH  Google Scholar 

  4. F. Buekenhout and X. Hubaut, “Locally polar spaces and related rank 3 graphs,”J. Algebra,45, 391–434 (1977).

    Article  MATH  Google Scholar 

  5. P. J. Cameron, J. M. Goethals, and J. J. Seidel, “Strongly regular graphs having strongly regular subconstituents,”J. Algebra,55, 257–280 (1978).

    Article  MATH  Google Scholar 

  6. P. J. Cameron, D. R. Hughes, and A. Pasini, “Extended generalized quadrangles,”Geom. Dedicat.,35 193–228 (1990).

    MATH  Google Scholar 

  7. F. de Clerk and H. van Maldeghem, “Some classes of rank 2 geometries,” In:Handbook of Incidence Geometry, Chapter 10. Elsevier Science (1995).

  8. A. D. Gardiner, C. D. Godsil, A. D. Hensel, and F. R. Gordon, “Second neighborhoods of strongly regular graphs,”Discrete Math.,103, 161–170 (1992).

    Article  MATH  Google Scholar 

  9. J. I. Hall, “Locally Petersen graphs,”J. Graph Theory,4, 173–187 (1980).

    Article  MATH  Google Scholar 

  10. J. I., Hall, “On copolar spaces and graphs,”Q. J. Math. Oxford, Ser. 2,33, 421–449 (1982).

    Article  MATH  Google Scholar 

  11. J. I. Hall and E. E. Shult, “Locally cotriangular graphs,”Geom. Dedicat.,18, 113–159 (1985).

    MATH  Google Scholar 

  12. D. Hughes and S. Hobart, “EpGs with minimal μ, II,”Geom. Dedicat.,42, 129–138 (1992).

    MATH  Google Scholar 

  13. V. V. Kabanov, “A characterization of triangular and lattice graphs,”Sib. Mat. Zh.,39, 1054–1059 (1998).

    MATH  Google Scholar 

  14. V. V. Kabanov and A. A. Makhnev, “Coedge regular graphs without 3-claws,”Mat. Zametki,60, 495–503 (1996).

    Google Scholar 

  15. V. V. Kabanov and A. A. Makhnev, “On separated graphs with some regularity conditions,”Mat. Sb.,187, 1–14 (1996).

    Article  Google Scholar 

  16. A. A. Makhnev, “On strongly regular extensions of generalized quadrangles,”Mat. Sb.,184, 123–132 (1993).

    Google Scholar 

  17. A. A. Makhnev, “Finite locallyGQ(3,3)-graphs,”Sib. Mat. Zh.,35, 1314–1324 (1994).

    Google Scholar 

  18. A. A. Makhnev, “LocallyGQ(e,6)-grpahs and geometries with short lines,”Discr. Mat.,10, 72–86 (1998).

    Google Scholar 

  19. A. A. Makhnev, “On extended partial geometries containing small μ-subgraphs,”Discr. Anal. Oper. Res.,3, 71–83 (1996).

    MATH  Google Scholar 

  20. A. A. Makhnev, “On pseudogeometric graphs of partial geometriespG 2(4,t),”Math. Sb.,187, 97–112 (1996).

    Google Scholar 

  21. A. A. Makhnev, “On regular Terwilliger graphs with μ=2,”Sib. Mat. Zh.,37, 1132–1134 (1996).

    Google Scholar 

  22. A. A. Makhnev, “Partial geometries and the Krein conditions,” In:Proc. Intern. Math. Congress, Bielefeld (1998), p. 282.

  23. A. A. Makhnev and D. V. Paduchikh, “On some class of regular graphs”,Proc. Intern. Coll. Combin. Graph Theory, Balatonlelle, Hungary (1996), p. 22.

  24. A. A. Makhnev and D. V. Paduchikh, “On the structure of connected locallyGQ(3, 9)-graphs,”Discr. Anal. Oper. Res.,5, 61–77 (1998).

    MATH  Google Scholar 

  25. A. A. Makhnev and D. V. Paduchikkh, “On 2-locally Seidel graphs,”Izv. Rossiisk. Akad. Nauk, Ser. Mat.,61, 67–80 (1997).

    Google Scholar 

  26. A. A. Makhnev and N. D. Zyulyarkina, “On strongly regular locally grid-graphs,”Discr. Mat.,5, 143–148 (1993).

    Google Scholar 

  27. R. Mathon, “A new family of partial geometries”, In:Finite Geometry and Combinatorics. Proc. Third Intern. Conf. Deinze, 18–24 May (1997).

  28. M. Mumata, “On a characterization of a class of regular graphs,”Osaka Math. J.,11, 389–400 (1974).

    Google Scholar 

  29. D. V. Paduchikh, “Influence of 2-neighborhoods on the structure of a graphs,”Math. Zametki,62, 892–897 (1997).

    Google Scholar 

  30. S. Payne and J. Thas,Finite Generalized Quadrangles, Pitman, Boston (1984).

    MATH  Google Scholar 

  31. D. Pasechnik, “The extensions of the generalized quadrangle of order (3,9),”Eur. J. Combin.,17, 751–755 (1996).

    Article  MATH  Google Scholar 

  32. D. Pasechnik, “The triangular extensions of a generalized quadrangle of order (3,3),”Simon Stevin,2, 509–518 (1995).

    MATH  Google Scholar 

  33. H. A. Wilbrink and A. E. Brouwer, “The (57, 14, 1) strongly regular graph does not exist,”Proc. Kon. Nederl. Akad., Ser. A,45, 117–121 (1983).

    Google Scholar 

  34. S. Yoshiara, “On some flag-transitive nonclassicalc-C 2-geometries,”Eur. J. Combin.,14, 59–77 (1993).

    Article  MATH  Google Scholar 

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 63, Algebra-13, 1999

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Makhnev, A.A. Partial geometries, their extensions, and related graphs. J Math Sci 102, 4009–4017 (2000). https://doi.org/10.1007/BF02673877

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