Geodesic
Graphs in which neighborhoods of vertices are isomorphic to the Hoffman–Singleton graph
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 2, pp. 143-161

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Connected graphs are studied in which neighborhoods of vertices are isomorphic to the Hoffman—Singleton graph (i.e., the strongly regular graph with parameters (50,7,0,1)). It is proved that a distance-regular graph in which neighborhoods of vertices are isomorphic to the Hoffman—Singleton graph has $\mu=2$.
Keywords: Hoffman-–Singleton graph, distance-regular graph, locally $\mathcal F$-graph. 
A. A. Makhnev. Graphs in which neighborhoods of vertices are isomorphic to the Hoffman–Singleton graph. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 2, pp. 143-161. http://geodesic.mathdoc.fr/item/TIMM_2009_15_2_a13/
@article{TIMM_2009_15_2_a13,
     author = {A. A. Makhnev},
     title = {Graphs in which neighborhoods of vertices are isomorphic to the {Hoffman{\textendash}Singleton} graph},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {143--161},
     year = {2009},
     volume = {15},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2009_15_2_a13/}
}
TY  - JOUR
AU  - A. A. Makhnev
TI  - Graphs in which neighborhoods of vertices are isomorphic to the Hoffman–Singleton graph
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2009
SP  - 143
EP  - 161
VL  - 15
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TIMM_2009_15_2_a13/
LA  - ru
ID  - TIMM_2009_15_2_a13
ER  - 
%0 Journal Article
%A A. A. Makhnev
%T Graphs in which neighborhoods of vertices are isomorphic to the Hoffman–Singleton graph
%J Trudy Instituta matematiki i mehaniki
%D 2009
%P 143-161
%V 15
%N 2
%U http://geodesic.mathdoc.fr/item/TIMM_2009_15_2_a13/
%G ru
%F TIMM_2009_15_2_a13

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

[2] Gavrilyuk A. L.,Makhnev A. A., “Grafy Tervilligera, v kotorykh okrestnost nekotoroi vershiny izomorfna grafu Petersena”, Dokl. RAN, 421:4 (2008), 445–448 | MR

[3] Makhnev A. A., “O grafakh, v kotorykh okrestnosti vershin izomorfny grafu Khofmana–Singltona”, Dokl. RAN, 422:6 (2008), 735–737 | MR

[4] Brouwer A. E., Haemers W. H., “The Gewirtz graph: an exercize in the theory of graph spectra”, Europ. J. Comb., 14:5 (1993), 397–407 | DOI | MR | Zbl

[5] Terwilliger P., “A new feasibility condition for distance-regular graphs”, Discrete Math., 61:2–3 (1986), 311–315 | DOI | MR | Zbl

[6] Haemers W. H., “Interlacing eigenvalues and graphs”, Linear Alg. Appl., 226–228 (1995), 593–616 | DOI | MR | Zbl