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1.
The core of a vertex-transitive complementary prism
Marko Orel, 2023, izvirni znanstveni članek

Opis: The complementary prism ▫$\Gamma \overline{\Gamma}$▫ is obtained from the union of a graph ▫$\Gamma$▫ and its complement ▫$\overline{\Gamma}$▫ where each pair of identical vertices in ▫$\Gamma$▫ and ▫$\overline{\Gamma}$▫ is joined by an edge. It generalizes the Petersen graph, which is the complementary prism of the pentagon. The core of a vertex-transitive complementary prism is studied. In particular, it is shown that a vertex-transitive complementary prism ▫$\Gamma \overline{\Gamma}$▫ is a core, i.e. all its endomorphisms are automorphisms, whenever ▫$\Gamma$▫ is a core or its core is a complete graph.
Ključne besede: graph homomorphism, complementary prism, self-complementary graph, vertex-transitive graph, core
Objavljeno v RUP: 06.11.2023; Ogledov: 1033; Prenosov: 6
.pdf Celotno besedilo (305,54 KB)

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Classification of cubic vertex-transitive tricirculants
Primož Potočnik, Micael Toledo, 2020, izvirni znanstveni članek

Ključne besede: graph, cubic, semiregular automorphism, tricirculant, vertex-transitive
Objavljeno v RUP: 03.01.2022; Ogledov: 1096; Prenosov: 41
.pdf Celotno besedilo (1,18 MB)

4.
Vertex-transitive graphs and their arc-types
Marston D. E. Conder, Tomaž Pisanski, Arjana Žitnik, 2017, izvirni znanstveni članek

Opis: Let ▫$X$▫ be a finite vertex-transitive graph of valency ▫$d$▫, and let ▫$A$▫ be the full automorphism group of ▫$X$▫. Then the arc-type of ▫$X$▫ is defined in terms of the sizes of the orbits of the stabiliser ▫$A_v$▫ of a given vertex ▫$v$▫ on the set of arcs incident with ▫$v$▫. Such an orbit is said to be self-paired if it is contained in an orbit ▫$\Delta$▫ of ▫$A$▫ on the set of all arcs of v$X$▫ such that v$\Delta$▫ is closed under arc-reversal. The arc-type of ▫$X$▫ is then the partition of ▫$d$▫ as the sum ▫$n_1 + n_2 + \dots + n_t + (m_1 + m_1) + (m_2 + m_2) + \dots + (m_s + m_s)$▫, where ▫$n_1, n_2, \dots, n_t$▫ are the sizes of the self-paired orbits, and ▫$m_1,m_1, m_2,m_2, \dots, m_s,m_s$▫ are the sizes of the non-self-paired orbits, in descending order. In this paper, we find the arc-types of several families of graphs. Also we show that the arc-type of a Cartesian product of two "relatively prime" graphs is the natural sum of their arc-types. Then using these observations, we show that with the exception of ▫$1+1$▫ and ▫$(1+1)$▫, every partition as defined above is \emph{realisable}, in the sense that there exists at least one vertex-transitive graph with the given partition as its arc-type.
Ključne besede: symmetry type, vertex-transitive graph, arc-transitive graph, Cayley graph, cartesian product, covering graph
Objavljeno v RUP: 02.01.2022; Ogledov: 1175; Prenosov: 20
.pdf Celotno besedilo (475,17 KB)

5.
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: 30.12.2021; Ogledov: 1233; Prenosov: 22
.pdf Celotno besedilo (275,74 KB)

6.
Some recent discoveries about half-arc-transitive graphs : dedicated to Dragan Marušič on the occasion of his 60th birthday
Marston D. E. Conder, Primož Potočnik, Primož Šparl, 2015, izvirni znanstveni članek

Opis: We present some new discoveries about graphs that are half-arc-transitive (that is, vertex- and edge-transitive but not arc-transitive). These include the recent discovery of the smallest half-arc-transitive 4-valent graph with vertex-stabiliser of order 4, and the smallest with vertex-stabiliser of order 8, two new half-arc-transitive 4-valent graphs with dihedral vertex-stabiliser ▫$D_4$▫ (of order 8), and the first known half-arc-transitive 4-valent graph with vertex-stabiliser of order 16 that is neither abelian nor dihedral. We also use half-arc-transitive group actions to provide an answer to a recent question of Delorme about 2-arc-transitive digraphs that are not isomorphic to their reverse.
Ključne besede: graph, edge-transitive, vertex-transitive, arc-transitive, half arc-transitive
Objavljeno v RUP: 30.12.2021; Ogledov: 1082; Prenosov: 17
.pdf Celotno besedilo (333,06 KB)

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Extremal edge-girth-regular graphs
Ajda Zavrtanik Drglin, Slobodan Filipovski, Robert Jajcay, Tom Raiman, 2021, izvirni znanstveni članek

Ključne besede: regular graph, girth, vertex-transitive graph
Objavljeno v RUP: 16.07.2021; Ogledov: 1643; Prenosov: 28
URL Povezava na celotno besedilo

9.
Vertex cover at distance on H-free graphs
Clément Jean Dallard, Mirza Krbezlija, Martin Milanič, 2021, objavljeni znanstveni prispevek na konferenci

Ključne besede: distance-k vertex cover, H-free graph, np-completeness, polynomial-time algorithm, dichotomy
Objavljeno v RUP: 16.07.2021; Ogledov: 1947; Prenosov: 31
URL Povezava na celotno besedilo

10.
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