Naslov
Construction of strongly regular graphs having an automorphism group of composite order

Autori
Crnković, Dean ; Maksimović, Marija

Izvornik
Contributions to Discrete Mathematics (1715-0868) 15 (2020), 1; 22-41

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

Ključne riječi
Strongly regular graph ; automorphism group ; orbit matrix

Sažetak
In this paper we outline a method for constructing strongly regular graphs from orbit matrices admitting an automorphism group of composite order. In 2011, C. Lam and M. Behbahani introduced the concept of orbit matrices of strongly regular graphs and developed an algorithm for the construction of orbit matrices of strongly regular graphs with a presumed automorphism group of prime order, and construction of corresponding strongly regular graphs. The method of constructing strongly regular graphs developed and employed in this paper is a generalization of that developed by C. Lam and M. Behbahani. Using this method we classify SRGs with parameters (49, 18, 7, 6) having an automorphism group of order six. Eleven of the SRGs with parameters (49, 18, 7, 6) constructed in that way are new. We obtain an additional 385 new SRGs(49, 18, 7, 6) by switching. Comparing the constructed graphs with previously known SRGs with these parameters, we conclude that up to isomorphism there are at least 727 SRGs with parameters (49, 18, 7, 6). Further, we show that there are no SRGs with parameters (99, 14, 1, 2) having an automorphism group of order six or nine, i.e. we rule out automorphism groups isomorphic to Z6, S3, Z9, or E9.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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