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2. On 3-isoregularity of multicirculantsKlavdija Kutnar, Dragan Marušič, Štefko Miklavič, 2025, izvirni znanstveni članek Opis: 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.
Ključne besede: 3-isoregularity, strongly regular graph, bicirculant, tricirculant
Objavljeno v RUP: 06.08.2025; Ogledov: 252; Prenosov: 3
 Celotno besedilo (233,35 KB) |
3. Semiregular automorphisms in vertex-transitive graphs with a solvable group of automorphismsDragan Marušič, 2017, izvirni znanstveni članek Opis: It has been conjectured that automorphism groups of vertex-transitive (di)graphs, and more generally 2-closures of transitive permutation groups, must necessarily possess a fixed-point-free element of prime order, and thus a non-identity element with all orbits of the same length, in other words, a semiregular element. The known affirmative answers for graphs with primitive and quasiprimitive groups of automorphisms suggest that solvable groups need to be considered if one is to hope for a complete solution of this conjecture. It is the purpose of this paper to present an overview of known results and suggest possible further lines of research towards a complete solution of the problem.
Ključne besede: solvable group, semiregular automorphism, fixed-point-free automorphism, polycirculant conjecture
Objavljeno v RUP: 03.01.2022; Ogledov: 1904; Prenosov: 23
Celotno besedilo (235,26 KB) |
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6. Hamilton cycles in primitive vertex-transitive graphs of order a product of two primes - the case PSL(2, q[sup]2) acting on cosets of PGL(2, q)Shao Fei Du, Klavdija Kutnar, Dragan Marušič, 2020, izvirni znanstveni članek Opis: A step forward is made in a long standing Lovász problem regarding hamiltonicity of vertex-transitive graphs by showing that every connected vertex-transitive graph of order a product of two primes arising from the group action of the projective special linear group PSL▫$(2, q^2)$▫ on cosets of its subgroup isomorphic to the projective general linear group PGL$(2, q)$ contains a Hamilton cycle.
Ključne besede: vertex-transitive graph, Hamilton cycle, automorphism group, orbital graph
Objavljeno v RUP: 20.07.2020; Ogledov: 2811; Prenosov: 53
Celotno besedilo (365,31 KB) |
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