1. Minimal directed strongly regular Cayley graphs over generalized dicyclic groupsYueli Han, Lu Lu, 2025, original scientific article Abstract: Let G be a group with identity element 1, and let S be a subset of G \ {1}. The subset S is called minimal if ⟨S⟩ = G and there exists an element s ∈ S such that ⟨S \ {s, s−1}⟩ ≠ G. In this paper, we completely determine all directed strongly regular Cayley graphs Cay(G, S) for any generalized dicyclic group G, provided that S is a minimal subset of G.
Keywords: directed strongly regular graph, Cayley graph, generalized dicyclic group
Published in RUP: 21.10.2025; Views: 329; Downloads: 2
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2. On 3-isoregularity of multicirculantsKlavdija Kutnar, Dragan Marušič, Štefko Miklavič, 2025, original scientific article Abstract: A graph is said to be k-isoregular if any two vertex subsets of cardinality at most k, that induce subgraphs of the same isomorphism type, have the same number of neighbors. It is shown that no 3-isoregular bicirculant (and more generally, no locally 3-isoregular bicirculant) of order twice an odd number exists. Further, partial results for bicirculants of order twice an even number as well as tricirculants of specific orders, are also obtained. Since 3-isoregular graphs are necessarily strongly regular, a motivation for the above result about bicirculants is that it brings us a step closer to obtaining a direct proof of a classical consequence of the Classification of Finite Simple Groups, that no simply primitive group of degree twice a prime exists for primes greater than 5.
Keywords: 3-isoregularity, strongly regular graph, bicirculant, tricirculant
Published in RUP: 06.08.2025; Views: 407; Downloads: 3
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3. Partial geometries with regular automorphism groups : master’s thesisAdisa Hodžić, 2024, master's thesis Keywords: (near-) linear space, projective plane, affine plane, partial geometry, generalized quadrangle, strongly regular graph, partial difference set, automorphism group
Published in RUP: 25.12.2024; Views: 1872; Downloads: 31
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