Geodesic
Distance-regular graph with the intersection array $\{45,30,7;1,2,27\}$ does not exist
Diskretnaya Matematika, Tome 25 (2013) no. 2, pp. 13-30
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{DM_2013_25_2_a2,
     author = {A. L. Gavrilyuk and A. A. Makhnev},
     title = {Distance-regular graph with the intersection array $\{45,30,7;1,2,27\}$ does not exist},
     journal = {Diskretnaya Matematika},
     pages = {13--30},
     year = {2013},
     volume = {25},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2013_25_2_a2/}
}
TY  - JOUR
AU  - A. L. Gavrilyuk
AU  - A. A. Makhnev
TI  - Distance-regular graph with the intersection array $\{45,30,7;1,2,27\}$ does not exist
JO  - Diskretnaya Matematika
PY  - 2013
SP  - 13
EP  - 30
VL  - 25
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/DM_2013_25_2_a2/
LA  - ru
ID  - DM_2013_25_2_a2
ER  - 
%0 Journal Article
%A A. L. Gavrilyuk
%A A. A. Makhnev
%T Distance-regular graph with the intersection array $\{45,30,7;1,2,27\}$ does not exist
%J Diskretnaya Matematika
%D 2013
%P 13-30
%V 25
%N 2
%U http://geodesic.mathdoc.fr/item/DM_2013_25_2_a2/
%G ru
%F DM_2013_25_2_a2
A. L. Gavrilyuk; A. A. Makhnev. Distance-regular graph with the intersection array $\{45,30,7;1,2,27\}$ does not exist. Diskretnaya Matematika, Tome 25 (2013) no. 2, pp. 13-30. http://geodesic.mathdoc.fr/item/DM_2013_25_2_a2/

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

[2] Godsil C. D., “Geometric distance-regular covers”, J. Math., 22:2 (1993), 31–38 | MR | Zbl

[3] Koolen J. H., Bang S., “On distance-regular graphs with smallest eigenvalue at least $-m$”, J. Combin. Theory, 100:6 (2010), 573–584 | DOI | MR | Zbl

[4] Blokhuis A., Brouwer A. E., “Determination of the distance-regular graphs without 3-claws”, Discrete Math., 163:1–3 (1997), 225–227 | DOI | MR | Zbl

[5] Bang S., Geometric distance-regular graphs without 4-claws, arXiv: 1101.0440 | MR

[6] Bang S., Koolen J. H., “On geometric distance-regular graphs”, European Journal of Combinatorics (to appear)

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