On Deza graphs with parameters of complement graphs to lattice and triangular graphs
Diskretnyj analiz i issledovanie operacij, Tome 20 (2013) no. 2, pp. 3-14.

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We study strictly Deza graphs obtained from the complements of lattice graphs, triangular graphs, Chang graphs, and Shrikhande graph by means of their automorphisms of order two. We show that these graphs are characterized by their parameters under the assumption on their local structure. Bibliogr. 11.
Keywords: Deza graph, involutive automorphism.
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S. V. Goryainov; L. V. Shalaginov. On Deza graphs with parameters of complement graphs to lattice and triangular graphs. Diskretnyj analiz i issledovanie operacij, Tome 20 (2013) no. 2, pp. 3-14. http://geodesic.mathdoc.fr/item/DA_2013_20_2_a0/

[1] Goryainov S. V., Shalaginov L. V., “O grafakh Deza na 14, 15 i 16 vershinakh”, Sib. elektron. mat. izv., 8 (2011), 105–115 | MR

[2] Kabanov V. V., Shalaginov L. V., “O grafakh Deza s parametrami reshëtchatykh grafov”, Tr. IMM UrO RAN, 16, no. 3, 2010, 117–120

[3] Shalaginov L. V., “O grafakh Deza s parametrami treugolnykh grafov”, Tr. IMM UrO RAN, 17, no. 1, 2011, 294–298

[4] Bose R. C., “Strongly regular graphs, partial geometries and partially balanced designs”, Pacific J. Math., 13 (1963), 389–419 | MR | Zbl

[5] Brouwer A. E., Cohen A. M., Neumaier A., Distance regular graphs, Springer-Verl., Berlin, 1989, 495 pp. | MR | Zbl

[6] Chang L. C., “The uniqueness and nonuniqueness of the triangular association scheme”, Sci. Record., 3 (1959), 604–613 | MR | Zbl

[7] Deza M., Deza A., “The ridge graph of the metric polytope and some relatives”, Polytopes: abstract, convex, and computational, NATO ASI Ser., 440, Kluwer Acad., New York, 1994, 359–372 | MR | Zbl

[8] Erickson M., Fernando S., Haemers W. H., Hardy D., Hemmeter J., “Deza graphs: a generalization of strongly regular graphs”, J. Comb. Des., 7 (1999), 359–405 | MR

[9] Higman D. G., “Finite permutations group of rank 3”, Math. Z., 86 (1964), 145–156 | MR | Zbl

[10] Hoffman A. J., “On the uniqueness of the triangular association scheme”, Ann. Math. Stat., 31 (1960), 492–497 | MR | Zbl

[11] Shrikhande S. S., “The uniqueness of the $L_2$ association scheme”, Ann. Math. Stat., 30 (1959), 781–798 | MR | Zbl