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Semiregular automorphisms in vertex-transitive graphs with a solvable group of automorphisms
Dragan 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: 722; Prenosov: 17
.pdf Celotno besedilo (235,26 KB)

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The automorphism groups of non-edge transitive rose window graphs
Edward Dobson, István Kovács, Štefko Miklavič, 2015, izvirni znanstveni članek

Opis: In this paper, we determine the full automorphism groups of rose window graphs that are not edge-transitive. As the full automorphism groups of edge-transitive rose window graphs have been determined, this complete the problem of calculating the full automorphism group of rose window graphs. As a corollary, we determine which rose window graphs are vertex-transitive. Finally, we determine the isomorphism classes of non-edge-transitive rose window graphs.
Ključne besede: rose window graphs, automorphism group, isomorphism problem, vertex-transitive graph
Objavljeno v RUP: 31.12.2021; Ogledov: 835; Prenosov: 18
.pdf Celotno besedilo (275,74 KB)

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A family of non-Cayley cores that are constructed from vertex-transitive or strongly regular self-complementary graphs
Marko Orel, 2021, objavljeni povzetek znanstvenega prispevka na konferenci

Ključne besede: cores, graph homomorphisms, automorphism group, self-complementary graphs
Objavljeno v RUP: 30.07.2021; Ogledov: 915; Prenosov: 72
URL Povezava na celotno besedilo
Gradivo ima več datotek! Več...

7.
A family of non-Cayley cores that are constructed from vertex-transitive or strongly regular self-complementary graphs
Marko Orel, 2021, objavljeni povzetek znanstvenega prispevka na konferenci

Ključne besede: cores, graph homomorphisms, automorphism group, self-complementary graphs
Objavljeno v RUP: 30.07.2021; Ogledov: 1119; Prenosov: 42
.pdf Celotno besedilo (1,01 MB)
Gradivo ima več datotek! Več...

8.
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: 1206; Prenosov: 46
.pdf Celotno besedilo (365,31 KB)

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