On Shilla Graphs of Diameter 4
DOI:
https://doi.org/10.17072/1993-0550-2026-2-20-29Keywords:
Shilla graph, distance-regular graphAbstract
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
Koolen J.H., Park J. Shilla distance-regular graphs // European Journal of Combinatorics. 2010. Vol. 31, № 8. P. 2064−2073.
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.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Александр Алексеевич Махнев , Мариана Малиловна Исакова

This work is licensed under a Creative Commons Attribution 4.0 International License.
Articles are published under license Creative Commons Attribution 4.0 International (CC BY 4.0).
