On graphs in which neighborhoods of vertices are strongly regular with parameters (85,14,3,2) or (325,54,3,10)
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 3, pp. 137-143
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 nonprincipal eigenvalue at most $t$ for a given positive integer$t$. This problem was solved earlier for $t=3$. In the case $t=4$, a reduction to graphs in which neighborhoods of vertices have parameters (352,26,0,2), (352,36,0,4), (243,22,1,2), (729,112,1,20), (204,28,2,4), (232,33,2,5), (676,108,2,20), (85,14,3,2), or (325,54,3,10) was obtained. In the present paper, we prove that a distance regular graph in which neighborhoods of vertices are strongly regular with parameters $(85,14,3,2)$ or $(325,54,3,10)$ has intersection array $\{85,70,1;1,14,85\}$ or $\{325,270,1;1,54,325\}$. In addition, we find possible automorphisms of a graph with intersection array $\{85,70,1;1,14,85\}$.
Keywords:
strongly regular graph, locally $\mathcal X$-graph, automorphism of a graph.
@article{TIMM_2016_22_3_a12,
author = {M. M. Isakova and A. A. Makhnev and A. A. Tokbaeva},
title = {On graphs in which neighborhoods of vertices are strongly regular with parameters (85,14,3,2) or (325,54,3,10)},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {137--143},
publisher = {mathdoc},
volume = {22},
number = {3},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2016_22_3_a12/}
}
TY - JOUR AU - M. M. Isakova AU - A. A. Makhnev AU - A. A. Tokbaeva TI - On graphs in which neighborhoods of vertices are strongly regular with parameters (85,14,3,2) or (325,54,3,10) JO - Trudy Instituta matematiki i mehaniki PY - 2016 SP - 137 EP - 143 VL - 22 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2016_22_3_a12/ LA - ru ID - TIMM_2016_22_3_a12 ER -
%0 Journal Article %A M. M. Isakova %A A. A. Makhnev %A A. A. Tokbaeva %T On graphs in which neighborhoods of vertices are strongly regular with parameters (85,14,3,2) or (325,54,3,10) %J Trudy Instituta matematiki i mehaniki %D 2016 %P 137-143 %V 22 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2016_22_3_a12/ %G ru %F TIMM_2016_22_3_a12
M. M. Isakova; A. A. Makhnev; A. A. Tokbaeva. On graphs in which neighborhoods of vertices are strongly regular with parameters (85,14,3,2) or (325,54,3,10). Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 3, pp. 137-143. http://geodesic.mathdoc.fr/item/TIMM_2016_22_3_a12/