Strongly regular graphs with parameters (37, 18, 8, 9) having nontrivial automorphisms

Crnković, Dean; Maksimović, Marija

doi:10.26493/2590-9770.1295.25b

Art Discrete Appl. Math.

2020

DOI: 10.26493/2590-9770.1295.25b

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Strongly regular graphs with parameters (37, 18, 8, 9) having nontrivial automorphisms

Dean Crnković

Marija Maksimović

Abstract: All strongly regular graphs having at most 36 vertices have been enumerated. Hence, the first open case is enumeration of the SRGs with parameters (37, 18, 8, 9). In this paper we show that there are exactly forty SRGs with parameters (37, 18, 8, 9) having nontrivial automorphisms. Comparing the constructed graphs with previously known SRGs with these parameters we conclude that six of the SRGs with parameters (37, 18, 8, 9) constructed in this paper are new, and that up to isomorphism there are at least 6766 … Show more

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2023

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On Some Regular Two-Graphs up to 50 Vertices

Maksimović

2023

Symmetry

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Regular two-graphs on up to 36 vertices are classified, and recently, the classification of regular 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 automorphism 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).

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On Some Regular Two-Graphs up to 50 Vertices

Maksimović

2023

Symmetry

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Strongly regular graphs with parameters (37, 18, 8, 9) having nontrivial automorphisms

Cited by 1 publication

References 9 publications

On Some Regular Two-Graphs up to 50 Vertices

On Some Regular Two-Graphs up to 50 Vertices

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