### AUTOMORPHISMS OF DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {25; 16; 1; 1; 8; 25}

#### Abstract

Makhnev and Samoilenko have found parameters of strongly regular graphs with no more than 1000 vertices, which may be neighborhoods of vertices in antipodal distance-regular graph of diameter 3 and with \(\lambda=\mu\). They proposed the program of investigation vertex-symmetric antipodal distance-regular graphs of diameter 3 with \(\lambda=\mu\), in which neighborhoods of vertices are strongly regular. In this paper we consider neighborhoods of vertices with parameters \((25,8,3,2)\).

#### Keywords

Strongly regular graph, Distance-regular graph

#### Full Text:

PDF#### References

- Makhnev A.A., Samoilenko M.S. Automorphisms of distance-regular graph with intersection array {121,100,1;1,20,121} // Proc. of the 47-th International Youth School-conference, Ekaterinburg, Russia, 2016, P. S21–S25. [in Russian]
- Isakova M.M., Makhnev A.A., Tokbaeva A.A. Automorphisms of distance-regular graph with intersection array {64,42,1;1,21,64} // Intern. Conf. on applied Math. and Physics. Abstracts. Nalchik 2017. P. 245–246. [in Russian]
- Belousov I.N. On automorphisms of distance-regular graph with intersection array {81,64,1;1,16,81} // Proceedings of Intern. Russian – Chinese Conf. 2015, Nalchik. P. 31–32. [in Russian]
- Makhnev A.A., Isakova M.M., Tokbaeva A.A. On graphs, in which neighbourhoods of vertices are strongly regular with parameters (85,14,1,2) or (325,54,3,10) // Trudy IMM UrO RAN, 2016. Vol. 22, no. 3, P. 137–143. [in Russian]
- Ageev P.S., Makhnev A.A. On automorphisms of distance-regular graphs with intersection array {99,84,1;1,14,99} // Doklady Mathematics, 2014. Vol. 90, no. 2, P. 525–528. DOI: 10.1134/S1064562414060015
- Makhnev A.A., Paduchikh D.V. Distance-regular graphs, in which neighbourhoods of vertices are strongly regular with the second eigenvalue at most 3 // Doklady Mathematics, 2015. Vol. 92, no. 2. P. 568–571. DOI: 10.1134/S1064562415050191
- Brouwer A.E., Cohen A.M., Neumaier A. Distance-Regular Graphs. New York: Springer-Verlag, 1989. 495 p. DOI: 10.1007/978-3-642-74341-2
- Gavrilyuk A.L., Makhnev A.A. On automorphisms of distance-regular graph with the intersection array {56,45,1;1,9,56} // Doklady Mathematics, 2010. Vol. 81, no. 3. P. 439–442. DOI: 10.1134/S1064562410030282
- Makhnev A.A., Paduchikh D.V., Tsiovkina L.Y. Arc-transitive distance-regular covers of cliques with \(\lambda=\mu\) // Proc. Steklov Inst. Math., 2014. Vol. 284, suppl. 1, P. S124–S134. DOI: 10.1134/S0081543814020114
- Zavarnitsin A.V. Finite simple groups with narrow prime spectrum // Siberian Electr. Math. Izv., 2009. Vol. 6. P. 1–12. [in Russian]

#### Article Metrics

Metrics Loading ...

### Refbacks

- There are currently no refbacks.