On Shilla Graphs of Diameter 4

Authors

  • Alexander A. Makhnev N. N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Acade-my of Sciences https://orcid.org/0000-0003-2868-6713
  • Mariana M. Isakova Kabardino-Balkarian State University named after H.M. Berbekov

DOI:

https://doi.org/10.17072/1993-0550-2026-2-20-29

Keywords:

Shilla graph, distance-regular graph

Abstract

It is proved that distance-regular graphs with intersection arrays {20, 18, 5, 1; 1, 1, 18, 20} and {25, 24, 2, 1; 1, 2, 24, 25} do not exist.

References

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Koolen J., Park J., Yu H. An inequality involving the second largest and smallest eigen-value of a distance-regular graph // Linear Algebra and Appl. 2011. Vol. 434:12, P. 2404–2412.

Brouwer A.E., Cohen A.M., Neumaier A. Distance-Regular Graphs. Berlin; Heidelberg; New York: Springer-Verlag, 1989. 495 p.

Soicher L. The uniqueness of a distance-regular graph with intersection array {32,27,8,1;1,4,27,32} and related results // Des. Codes Cryptogr. 2012. Vol. 84. P. 101–108.

Jurishich A., Koolen J. Krein parameters and antipodal tight graphs with diameter 3 and 4 // Discrete Mathematics. 2002. Vol. 244. P. 181–202.

Coolsaet K., Jurishich A. Using equality in the Krein conditions to prove nonexistence of sertain distance-regular graphs // J. Comb. Theory, Series A. 2008. Vol. 115. P. 1086–1095.

Jurishic A., Vidali J. Extremal 1-codes in distance-regular graphs of diameter 3 // Des. Codes Cryptogr. 2012. Vol. 65. P. 29–47.

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Published

2026-07-13

How to Cite

On Shilla Graphs of Diameter 4. (2026). BULLETIN OF PERM UNIVERSITY. MATHEMATICS. MECHANICS. COMPUTER SCIENCE, 2 (73), 20-29. https://doi.org/10.17072/1993-0550-2026-2-20-29

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