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1.
Rose window graphs underlying rotary maps
István Kovács, Klavdija Kutnar, János Ruff, 2010, published scientific conference contribution

Abstract: Given natural numbers ▫$n \ge 3$▫ and ▫$1 \le a$▫, ▫$r \le n-1$▫, the rose window graph ▫$R_n(a,r)$▫ is a quartic graph with vertex set ▫$\{x_i \vert\; i \in {\mathbb Z}_n \} \cup \{y_i \vert\; i \in {\mathbb Z}_n \}$▫ and edge set ▫$\{\{x_i, x_{i+1}\} \vert\; i \in {\mathbb Z}_n \} \cup \{\{y_i, y_{i+1}\} \vert\; i \in {\mathbb Z}_n \} \cup \{\{x_i, y_i\} \vert\; i \in {\mathbb Z}_n\} \cup \{\{x_{i+a}, y_i\} \vert\; i \in {\mathbb Z}_n \}$▫. In this paper rotary maps on rose window graphs are considered. In particular, we answer the question posed in [S. Wilson, Rose window graphs, Ars Math. Contemp. 1 (2008), 7-19. http://amc.imfm.si/index.php/amc/issue/view/5] concerning which of these graphs underlie a rotary map.
Found in: ključnih besedah
Summary of found: ......
Keywords: graph theory, rotary map, edge-transitive graph, covering graph, voltage graph
Published: 15.10.2013; Views: 1732; Downloads: 55
URL Full text (0,00 KB)

2.
Classification of edge-transitive rose window graphs
István Kovács, Klavdija Kutnar, Dragan Marušič, 2010, original scientific article

Abstract: Given natural numbers ▫$n \ge 3$▫ and ▫$1 \le a$▫, ▫$r \le n-1$▫, the rose window graph ▫$R_n(a,r)$▫ is a quartic graph with vertex set ▫$\{x_i \vert i \in {\mathbb Z}_n\} \cup \{y_i \vert i \in {\mathbb Z}_n\}$▫ and edge set ▫$\{\{x_i, x_{i+1}\} \vert i \in {\mathbb Z}_n\} \cup \{\{y_i, y_{i+r}\} \vert i \in {\mathbb Z}_n\} \cup \{\{x_i, y_i\} \vert i \in {\mathbb Z}_n\} \cup \{\{x_{i+a}, y_i\} \vert i \in {\mathbb Z}_n\}$▫. In this article a complete classification of edge-transitive rose window graphs is given, thus solving one of three open problems about these graphs posed by Steve Wilson in 2001.
Found in: ključnih besedah
Summary of found: Zadetek v naslovu
Keywords: group, graph, rose window, vertex-transitive, edge-transitive, arc-transitive
Published: 15.10.2013; Views: 1445; Downloads: 57
URL Full text (0,00 KB)

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4.
Edge regular graph products
Boštjan Frelih, Štefko Miklavič, 2013, original scientific article

Found in: ključnih besedah
Summary of found: Zadetek v naslovu
Keywords: edge regular graph, strong product, lexicographic product, deleted lexicographic product, co-normal product
Published: 15.10.2013; Views: 1452; Downloads: 33
URL Full text (0,00 KB)

5.
Regular embeddings of cycles with multiple edges revisited
Martin Škoviera, Roman Nedela, Kan Hu, Naer Wang, 2015, original scientific article

Abstract: Regularne vložitve ciklov z večkratnimi povezavami se pojavljajo v literaturi že kar nekaj časa, tako v topološki teoriji grafov kot tudi izven nje. Ta članek izriše kompletno podobo teh zemljevidov na ta način, da povsem opiše, klasificira in enumerira regularne vložitve ciklov z večkratnimi povezavami tako na orientabilnih kot tudi na neorientabilnih ploskvah. Večina rezultatov je sicer znana v tej ali oni obliki, toda tu so predstavljeni iz poenotenega zornega kota, osnovanega na teoriji končnih grup. Naš pristop daje dodatno informacijo tako o zemljevidih kot o njihovih grupah avtomorfizmov, priskrbi pa tudi dodaten vpogled v njihove odnose.
Found in: ključnih besedah
Summary of found: Zadetek v naslovu
Keywords: regularna vložitev, večkratna povezava, Hölderjev izrek, Möbiusov zemljevid, regular embedding, multiple edge, Hölder's Theorem, Möbius map
Published: 15.10.2015; Views: 1159; Downloads: 62
URL Full text (0,00 KB)

6.
On cyclic edge-connectivity of fullerenes
Dragan Marušič, Klavdija Kutnar, 2008, original scientific article

Abstract: A graph is said to be cyclically ▫$k$▫-edge-connected, if at least ▫$k$▫ edges must be removed to disconnect it into two components, each containing a cycle. Such a set of ▫$k$▫ edges is called a cyclic-k-edge cutset and it is called a trivial cyclic-k-edge cutset if at least one of the resulting two components induces a single ▫$k$▫-cycle. It is known that fullerenes, that is, 3-connected cubic planar graphs all of whose faces are pentagons and hexagons, are cyclically 5-edge-connected. In this article it is shown that a fullerene ▫$F$▫ containing a nontrivial cyclic-5-edge cutset admits two antipodal pentacaps, that is, two antipodal pentagonal faces whose neighboring faces are also pentagonal. Moreover, it is shown that ▫$F$▫ has a Hamilton cycle, and as a consequence at least ▫$15 \cdot 2^{n/20-1/2}$▫ perfect matchings, where ▫$n$▫ is the order of ▫$F$▫.
Found in: ključnih besedah
Summary of found: Zadetek v naslovu
Keywords: graph, fullerene graph, cyclic edge-connectivity, hamilton cycle, perfect matching
Published: 03.04.2017; Views: 824; Downloads: 96
URL Full text (0,00 KB)

7.
On two extensions of equimatchable graphs
Zakir Deniz, Tinaz Ekim, Tatiana Romina Hartinger, Martin Milanič, Mordechai Shalom, 2017, original scientific article

Found in: ključnih besedah
Summary of found: ......
Keywords: minimum maximal matching, equimatchable graph, edge dominating set, Gallai-Edmonds decomposition, parameterized complexity
Published: 29.01.2018; Views: 702; Downloads: 103
URL Full text (0,00 KB)

8.
Edge-girth-regular graphs
Robert Jajcay, György Kiss, Štefko Miklavič, 2018, original scientific article

Found in: ključnih besedah
Summary of found: Zadetek v naslovu
Keywords: girth, edge-regular graph, edge-girth-regular graph
Published: 18.05.2018; Views: 678; Downloads: 126
URL Full text (0,00 KB)

9.
Algebraic graph theory
Ademir Hujdurović, 2018, other educational material

Found in: ključnih besedah
Summary of found: ......
Keywords: graph, automorphism, automorphism group, vertex-transitive graph, edge-transitive graph, arc-transitive graph, Cayley graph
Published: 17.09.2018; Views: 526; Downloads: 9
URL Full text (0,00 KB)

10.
The classification of 2-extendable edge-regular graphs with diameter 2
Klavdija Kutnar, Dragan Marušič, Štefko Miklavič, Primož Šparl, 2019, original scientific article

Found in: ključnih besedah
Summary of found: Zadetek v naslovu
Keywords: edge-regular, diameter, 2-extendable
Published: 13.02.2019; Views: 259; Downloads: 21
URL Full text (0,00 KB)

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