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: 876; Downloads: 9
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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: 919; Downloads: 6
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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: 2521; Downloads: 59
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5. Konstrukcije novih superrazredov ukrivljenih funkcij in nadaljnje konstrukcije kriptografsko pomembnih preslikav izven M# : doktorska disertacijaAmar Bapić, 2022, doctoral dissertation Keywords: vecotorial bent function, class inclusion, complete Maiorana-McFaralnd class, MNBC functions, secondary constructions, weakly/almost strongly/strongly outside M#, 4-decomposition, SC and CD class, direct and indirect sum
Published in RUP: 12.12.2022; Views: 4487; Downloads: 41
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6. Strong cliques in diamond-free graphsNina Chiarelli, Berenice Martínez-Barona, Martin Milanič, Jérôme Monnot, Peter Muršič, 2020, original scientific article Keywords: maximal clique, maximal stable set, diamond-free graph, strong clique, simplicial clique, strongly perfect graph, CIS graph, NP-hard problem, polynomial-time algorithm, Erdős-Hajnal property
Published in RUP: 17.12.2020; Views: 4607; Downloads: 164
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10. Hamilton cycle and Hamilton path extendability of Cayley graphs on abelian groupsŠtefko Miklavič, Primož Šparl, 2012, original scientific article Abstract: In this paper the concepts of Hamilton cycle (HC) and Hamilton path (HP) extendability are introduced. A connected graph ▫$\Gamma$▫ is ▫$n$▫-HC-extendable if it contains a path of length ▫$n$▫ and if every such path is contained in some Hamilton cycle of ▫$\Gamma$▫. Similarly, ▫$\Gamma$▫ is weakly ▫$n$▫-HP-extendable if it contains a path of length ▫$n$▫ and if every such path is contained in some Hamilton path of ▫$\Gamma$▫. Moreover, ▫$\Gamma$▫ is strongly ▫$n$▫-HP-extendable if it contains a path of length ▫$n$▫ and if for every such path $P$ there is a Hamilton path of ▫$\Gamma$▫ starting with ▫$P$▫. These concepts are then studied for the class of connected Cayley graphs on abelian groups. It is proved that every connected Cayley graph on an abelian group of order at least three is 2-HC-extendable and a complete classification of 3-HC-extendable connected Cayley graphs of abelian groups is obtained. Moreover, it is proved that every connected Cayley graph on an abelian group of order at least five is weakly 4-HP-extendable.
Keywords: graph theory, Hamilton cycle, Hamilton path, n-HC-extendable, strongly n-HP-extendable, weakly n-HP-extendable, Cayley graph, abelian group
Published in RUP: 15.10.2013; Views: 5871; Downloads: 164
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