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1.
The Sierpiński product of graphs
Jurij Kovič, Tomaž Pisanski, Sara Sabrina Zemljič, Arjana Žitnik, 2023, izvirni znanstveni članek

Opis: In this paper we introduce a product-like operation that generalizes the construction of the generalized Sierpiński graphs. Let ▫$G, \, H$▫ be graphs and let ▫$f: V(G) \to V(H)$▫ be a function. Then the Sierpiński product of graphs ▫$G$▫ and ▫$H$▫ with respect to ▫$f$▫, denoted by ▫$G\otimes_f H$▫, is defined as the graph on the vertex set ▫$V(G) \times V(H)$▫, consisting of ▫$|V(G)|$▫ copies of ▫$H$▫; for every edge ▫$\{g, g'\}$▫ of ▫$G▫$ there is an edge between copies ▫$gH$▫ and ▫$g'H$▫ of form ▫$\{(g, f(g'), (g', f(g))\}$▫. Some basic properties of the Sierpiński product are presented. In particular, we show that the graph ▫$G\otimes_f H$▫ is connected if and only if both graphs ▫$G$▫ and ▫$H$▫ are connected and we present some conditions that ▫$G, \, H$▫ must fulfill for ▫$G\otimes_f H$▫ to be planar. As for symmetry properties, we show which automorphisms of ▫$G$▫ and ▫$H$▫ extend to automorphisms of ▫$G\otimes_f H$▫. In several cases we can also describe the whole automorphism group of the graph ▫$G\otimes_f H$▫. Finally, we show how to extend the Sierpiński product to multiple factors in a natural way. By applying this operation ▫$n$▫ times to the same graph we obtain an alternative approach to the well-known ▫$n$▫-th generalized Sierpiński graph.
Ključne besede: Sierpiński graphs, graph products, connectivity, planarity, symmetry
Objavljeno v RUP: 06.11.2023; Ogledov: 253; Prenosov: 3
.pdf Celotno besedilo (526,44 KB)

2.
Genetic data are crucial to conserve and manage wildlife in Southeast Europe
Elena Bužan, 2021, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Ključne besede: genetic diversity, molecular markers, connectivity, ungulates, mesopredators
Objavljeno v RUP: 18.10.2021; Ogledov: 1010; Prenosov: 9
URL Povezava na celotno besedilo

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On cyclic edge-connectivity of fullerenes
Klavdija Kutnar, Dragan Marušič, 2008, izvirni znanstveni članek

Opis: 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 ▫$F$▫.
Ključne besede: graph, fullerene graph, cyclic edge-connectivity, hamilton cycle, perfect matching
Objavljeno v RUP: 03.04.2017; Ogledov: 2042; Prenosov: 138
URL Povezava na celotno besedilo

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The price of connectivity for cycle transversals
Tatiana Romina Hartinger, Matthew Johnson, Martin Milanič, Daniël Paulusma, 2015, objavljeni znanstveni prispevek na konferenci

Ključne besede: price of connectivity, hereditary graph class, path, cycle, transversal
Objavljeno v RUP: 08.08.2016; Ogledov: 2802; Prenosov: 121
URL Povezava na celotno besedilo

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