The Koolen-Park bound and distance-regular graphs without $m$-clavs
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2022), pp. 64-69.

Voir la notice de l'article provenant de la source Math-Net.Ru

Using the Koolen-Park bound, we prove that distance-regular graphs with intersection arrays $\{83,54,21;1,6,63\}$, $\{80,54,12;1,6,60\}$ and $\{93,64,24;1,12,62\}$ do not exist.
Keywords: distance-regular graph, Koolen-Pack boundary
Mots-clés : $m$-clav.
@article{IVM_2022_9_a5,
     author = {A. A. Makhnev and Wenbin Guo and K. S. Efimov},
     title = {The {Koolen-Park} bound and distance-regular graphs without $m$-clavs},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {64--69},
     publisher = {mathdoc},
     number = {9},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_9_a5/}
}
TY  - JOUR
AU  - A. A. Makhnev
AU  - Wenbin Guo
AU  - K. S. Efimov
TI  - The Koolen-Park bound and distance-regular graphs without $m$-clavs
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2022
SP  - 64
EP  - 69
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2022_9_a5/
LA  - ru
ID  - IVM_2022_9_a5
ER  - 
%0 Journal Article
%A A. A. Makhnev
%A Wenbin Guo
%A K. S. Efimov
%T The Koolen-Park bound and distance-regular graphs without $m$-clavs
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2022
%P 64-69
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2022_9_a5/
%G ru
%F IVM_2022_9_a5
A. A. Makhnev; Wenbin Guo; K. S. Efimov. The Koolen-Park bound and distance-regular graphs without $m$-clavs. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2022), pp. 64-69. http://geodesic.mathdoc.fr/item/IVM_2022_9_a5/

[1] Brouwer A.E., Cohen A.M., Neumaier A., Distance-Regular Graphs, Springer-Verlag, Berlin-Heidelberg-New York, 1989 | MR | Zbl

[2] Koolen J.H., Park J., “Shilla distance-regular graphs”, Europ. J. Comb., 31:8 (2010), 2064–2073 | DOI | MR | Zbl

[3] Gavrilyuk A.L., Makhnev A.A., “Distance-regular graph with the intersection array $\{45,30,7;1,2,27\}$ does not exist”, Discr. Math. Appl., 23:3–4 (2013), 225–244 | MR | Zbl

[4] Gavrilyuk A.L., “Distance-regular graphs with the intersection arrays $\{55,36,11;1,4,45\}$ and $\{56,36,9;1,3,48\}$ do not exist”, Dokl. Math., 84:1 (2011), 444–446 | DOI | MR | Zbl

[5] Gavrilyuk A.L., Makhnev A.A., “Distance-regular graphs with intersection arrays $\{52,35,16;1,4,28\}$ and $\{69,48,24;1,4,46\}$ do not exist”, Designs Codes and Cryptography, 65:1–2 (2012), 49–54 | DOI | MR | Zbl

[6] Bang S., “Geometric distance-regular graphs without $4$-claws”, Linear Algebra Appl., 438:1 (2013), 37–46 | DOI | MR | Zbl