Geodesic
Extensions of pseudogeometric graphs for $pG_{s-5}(s,t)$
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 3, pp. 35-42 
A. K. Gutnova; A. A. Makhnev. Extensions of pseudogeometric graphs for $pG_{s-5}(s,t)$. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 3, pp. 35-42. http://geodesic.mathdoc.fr/item/VMJ_2016_18_3_a4/
@article{VMJ_2016_18_3_a4,
     author = {A. K. Gutnova and A. A. Makhnev},
     title = {Extensions of pseudogeometric graphs for~$pG_{s-5}(s,t)$},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {35--42},
     year = {2016},
     volume = {18},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2016_18_3_a4/}
}
TY  - JOUR
AU  - A. K. Gutnova
AU  - A. A. Makhnev
TI  - Extensions of pseudogeometric graphs for $pG_{s-5}(s,t)$
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2016
SP  - 35
EP  - 42
VL  - 18
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMJ_2016_18_3_a4/
LA  - ru
ID  - VMJ_2016_18_3_a4
ER  - 
%0 Journal Article
%A A. K. Gutnova
%A A. A. Makhnev
%T Extensions of pseudogeometric graphs for $pG_{s-5}(s,t)$
%J Vladikavkazskij matematičeskij žurnal
%D 2016
%P 35-42
%V 18
%N 3
%U http://geodesic.mathdoc.fr/item/VMJ_2016_18_3_a4/
%G ru
%F VMJ_2016_18_3_a4

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

J. Koolen posed the problem of studying distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with the second eigenvalue $\leq t$ for a given positive integer $t$. This problem is reduced to the description of distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with non-principal eigenvalue $t$ for $t=1,2,\dots$ In the article by A. K. Gutnova and A. A. Makhnev "Extensions of pseudogeometrical graphs for $pG_{s-4}(s,t)$" the Koolen problem was solved for $t=4$ and for pseudogeometrical neighborhoods of vertices. In the article of A. A. Makhnev “Strongly regular graphs with nonprincipal eigenvalue 5 and its extensions” the Koolen problem for $t=5$ was reduced to the case where the neighborhoods of vertices are exceptional graphs. In this paper intersection arrays for distance-regular graphs whose local subgraphs are exceptional pseudogeometric graphs for $pG_{s-5}(s,t)$.

[1] Gutnova A. K., Makhnev A. A., “Rasshireniya psevdogeometricheskikh grafov dlya $pG_{s-4}(s,t)$”, Vladikavk. mat. zhurn., 17:1 (2015), 21–30

[2] Makhnev A. A., “Strongly regular graphs with nonprincipal eigenvalue 5 and its extensions”, International conference “Groups and Graphs, Algorithms and Automata”, Abstracts, Yekaterinburg, 2015, 68

[3] Koolen J. H., Park J., “Distance-regular graphs with $a_1$ or $c_2$ at least half the valency”, J. Comb. Theory Ser. A, 119 (2012), 546–555 | DOI | MR | Zbl

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

[5] Brouwer A. E., Haemers W. H., Spectra of graphs (course notes), http://www.win.tue.nl/~aeb/

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

[7] Jurisic A., Koolen J., “Classification of the family $AT4(qs,q,q)$ of antipodal tight graphs”, J. Comb. Theory, 118:3 (2011), 842–852 | DOI | MR | Zbl