Automorphisms of strongly regular graphs with parameters $(1305,440,115,165)$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 23 (2017) no. 4, pp. 232-242
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A graph $\varGamma$ is called $t$-isoregular if, for any $i\le t$ and any $i$-vertex subset $S$, the number $\varGamma(S)$ depends only on the isomorphism class of the subgraph induced by $S$. A graph $\varGamma$ on $v$ vertices is called absolutely isoregular if it is $(v-1)$-isoregular. It is known that each $5$-isoregular graph is absolutely isoregular, and such graphs have been fully described. Each exactly $4$-isoregular graph is either a pseudogeometric graph for pG$_r(2r,2r^3+3r^2-1)$ or its complement. By Izo$(r)$ we denote a pseudogeometric graph for pG$_r(2r,2r^3+3r^2-1)$. Graphs Izo$(r)$ do not exist for an infinite set of values of $r$ ($r=3,4,6,10,\ldots$). The existence of Izo$(5)$ is unknown. In this work we find possible automorphisms for the neighborhood of an edge from Izo$(5)$.
Keywords:
isoregular graph, strongly regular graph, pseudogeometric graph.
@article{TIMM_2017_23_4_a21,
author = {A. A. Makhnev and D. V. Paduchikh and M. M. Khamgokova},
title = {Automorphisms of strongly regular graphs with parameters $(1305,440,115,165)$},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {232--242},
publisher = {mathdoc},
volume = {23},
number = {4},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2017_23_4_a21/}
}
TY - JOUR AU - A. A. Makhnev AU - D. V. Paduchikh AU - M. M. Khamgokova TI - Automorphisms of strongly regular graphs with parameters $(1305,440,115,165)$ JO - Trudy Instituta matematiki i mehaniki PY - 2017 SP - 232 EP - 242 VL - 23 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2017_23_4_a21/ LA - ru ID - TIMM_2017_23_4_a21 ER -
%0 Journal Article %A A. A. Makhnev %A D. V. Paduchikh %A M. M. Khamgokova %T Automorphisms of strongly regular graphs with parameters $(1305,440,115,165)$ %J Trudy Instituta matematiki i mehaniki %D 2017 %P 232-242 %V 23 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2017_23_4_a21/ %G ru %F TIMM_2017_23_4_a21
A. A. Makhnev; D. V. Paduchikh; M. M. Khamgokova. Automorphisms of strongly regular graphs with parameters $(1305,440,115,165)$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 23 (2017) no. 4, pp. 232-242. http://geodesic.mathdoc.fr/item/TIMM_2017_23_4_a21/