Geodesic
Automorphisms of Higman graphs with $\mu=6$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 184-209 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We call a strongly regular graph with $v=\binom m2$ and $k=2(m-2)$ a Higman graph. In Higman graphs, the parameter $\mu$ takes values 4, 6, 7, and 8. We find possible orders of automorphisms of Higman graphs with $\mu =6$ and study the structure of fixed-point subgraphs of these automorphisms.
Keywords: graph, fixed-point subgraph.
Mots-clés : automorphism 
@article{TIMM_2014_20_2_a15,
     author = {N. D. Zyulyarkina and A. A. Makhnev},
     title = {Automorphisms of {Higman} graphs with~$\mu=6$},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {184--209},
     year = {2014},
     volume = {20},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a15/}
}
TY  - JOUR
AU  - N. D. Zyulyarkina
AU  - A. A. Makhnev
TI  - Automorphisms of Higman graphs with $\mu=6$
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2014
SP  - 184
EP  - 209
VL  - 20
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a15/
LA  - ru
ID  - TIMM_2014_20_2_a15
ER  - 
%0 Journal Article
%A N. D. Zyulyarkina
%A A. A. Makhnev
%T Automorphisms of Higman graphs with $\mu=6$
%J Trudy Instituta matematiki i mehaniki
%D 2014
%P 184-209
%V 20
%N 2
%U http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a15/
%G ru
%F TIMM_2014_20_2_a15
N. D. Zyulyarkina; A. A. Makhnev. Automorphisms of Higman graphs with $\mu=6$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 184-209. http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a15/

[1] Higman D. G., “Characterization of families of rank 3 permutation groups by the subdegrees, I”, Arch. Math., 21 (1970), 151–156 | DOI | MR | Zbl

[2] Liebeck M. W., Saxl J., “The finite primitive permutation groups of rank 3”, Bull. London Math. Soc., 18:2 (1986), 165–172 | DOI | MR | Zbl

[3] Zyulyarkin N. D., Makhnev A. A., “Avtomorfizmy polutreugolnykh grafov, imeyuschikh $\mu=6$”, Dokl. AN, 426:4 (2009), 439–442 | MR | Zbl

[4] Cameron P., Permutation Groups, London Math. Soc. Student Texts, 45, Cambr. Univ. Press, Cambridge, 1999, 220 pp. | MR | Zbl

[5] Makhnev A. A., Tokbaeva A. A., “Ob avtomorfizmakh silno regulyarnogo grafa s parametrami (76,35,18,14)”, Tr. In-ta matematiki i mekhaniki UrO RAN, 16, no. 3, 2010, 185–194

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

[7] Mac̆aj M., S̆irán̆ J., “Search for properties of the missing Moore graph”, Linear Algebra Appl., 432:9 (2010), 2381–2398 | DOI | MR

[8] Spence E., “Regular two-graphs on 36 vertices”, Linear Algebra Appl., 226/228 (1995), 459–497 | DOI | MR | Zbl