Naslov
On Some Regular Two-Graphs up to 50 Vertices

Autori
Maksimović, Marija

Izvornik
Symmetry (2073-8994) 15 (2023), 2; 408, 17

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
orbit matrices ; graphs ; two-graphs ; regular two-graphs ; strongly regular graphs

Sažetak
Regular two-graphs on up to 36 vertices are classified, and recently, the classification of reg- ular two-graphs on 38 and 42 vertices having at least one descendant with a nontrivial automorphism group has been performed. The first unclassified cases are those on 46 and 50 vertices. It is known that there are at least 97 regular two-graphs on 46 vertices leading to 2104 descendants and 54 regular two- graphs on 50 vertices leading to 785 descendants. In this paper, we classified all strongly regular graphs with parameters (45, 22, 10, 11), (49, 24, 11, 12), and (50, 21, 8, 9) that have Z6 as the automor- phism group and constructed regular two-graphs from SRGs (45, 22, 10, 11), SRGs (49, 24, 11, 12), and SRGs (50, 21, 8, 9) that have automorphisms of order six. In this way, we enumerated all regular two-graphs on up to 50 vertices that have at least one descendant with an automorphism group of order six or at least one strongly regular graph associated with an automorphism group of order six. We found 236 new regular two-graphs on 46 vertices leading to 3172 new SRG (45, 22, 10, 11) and 51 new regular two-graphs on 50 vertices leading to 398 new SRG (49, 24, 11, 12).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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