Graphs in which local subgraphs are strongly regular with second eigenvalue 5
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 188-200
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J. Koolen proposed the problem of studying distance-regular graphs in which the neighborhoods of vertices are strongly regular graphs with second eigenvalue $\le t$ for a given positive integer $t$. Earlier Koolen's problem was solved for $t=4$. We complete the classification of distance-regular graphs in which the neighborhoods of vertices are strongly regular graphs with second eigenvalue $r$, where $4$$r\le5$.
Keywords:
strongly regular graph, eigenvalue, distance-regular graph.
@article{TIMM_2016_22_4_a17,
author = {A. A. Makhnev and D. V. Paduchikh},
title = {Graphs in which local subgraphs are strongly regular with second eigenvalue 5},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {188--200},
publisher = {mathdoc},
volume = {22},
number = {4},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a17/}
}
TY - JOUR AU - A. A. Makhnev AU - D. V. Paduchikh TI - Graphs in which local subgraphs are strongly regular with second eigenvalue 5 JO - Trudy Instituta matematiki i mehaniki PY - 2016 SP - 188 EP - 200 VL - 22 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a17/ LA - ru ID - TIMM_2016_22_4_a17 ER -
%0 Journal Article %A A. A. Makhnev %A D. V. Paduchikh %T Graphs in which local subgraphs are strongly regular with second eigenvalue 5 %J Trudy Instituta matematiki i mehaniki %D 2016 %P 188-200 %V 22 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a17/ %G ru %F TIMM_2016_22_4_a17
A. A. Makhnev; D. V. Paduchikh. Graphs in which local subgraphs are strongly regular with second eigenvalue 5. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 188-200. http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a17/