1. Classification of cubic tricirculant nut graphsIvan Damnjanović, Nino Bašić, Tomaž Pisanski, Arjana Žitnik, 2024, izvirni znanstveni članek Povzetek: A nut graph is a simple graph whose adjacency matrix has the eigenvalue zero with multiplicity one such that its corresponding eigenvector has no zero entries. It is known that there exist no cubic circulant nut graphs. A bicirculant (resp. tricirculant) graph is defined as a graph that admits a cyclic group of automorphisms having two (resp. three) orbits of vertices of equal size. We show that there exist no cubic bicirculant nut graphs and we provide a full classification of cubic tricirculant nut graphs. Ključne besede: bicirculant, tricirculant, eigenvalue Objavljeno v DiRROS: 24.01.2025; Ogledov: 242; Prenosov: 135
Celotno besedilo (491,37 KB) Gradivo ima več datotek! Več... |
2. The Sierpiński product of graphsJurij Kovič, Tomaž Pisanski, Sara Sabrina Zemljič, Arjana Žitnik, 2023, izvirni znanstveni članek Povzetek: 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 DiRROS: 19.03.2024; Ogledov: 926; Prenosov: 585
Celotno besedilo (533,30 KB) Gradivo ima več datotek! Več... |
3. Design of coiled-coil protein-origami cages that self-assemble in vitro and in vivoAjasja Ljubetič, Fabio Lapenta, Helena Gradišar, Igor Drobnak, Jana Aupič, Žiga Strmšek, Duško Lainšček, Iva Hafner Bratkovič, Andreja Majerle, Nuša Krivec, Mojca Benčina, Tomaž Pisanski, Tanja Ćirković-Veličković, Adam Round, José María Carazo, Roberto Melero, Roman Jerala, 2017, izvirni znanstveni članek Objavljeno v DiRROS: 17.04.2018; Ogledov: 5123; Prenosov: 3197
Celotno besedilo (741,03 KB) Gradivo ima več datotek! Več... |
4. Design principles for rapid folding of knotted DNA nanostructuresVid Kočar, John S. Schreck, Slavko Čeru, Helena Gradišar, Nino Bašić, Tomaž Pisanski, Jonathan P. K. Doye, Roman Jerala, 2016, izvirni znanstveni članek Povzetek: Knots are some of the most remarkable topological features in nature. Self-assembly of knotted polymers without breaking or forming covalent bonds is challenging, as the chain needs to be threaded through previously formed loops in an exactly defined order. Here we describe principles to guide the folding of highly knotted single-chain DNA nanostructures as demonstrated on a nano-sized square pyramid. Folding of knots is encoded by the arrangement of modules of different stability based on derived topological and kinetic rules. Among DNA designs composed of the same modules and encoding the same topology, only the one with the folding pathway designed according to the "free-end" rule folds efficiently into the target structure. Besides high folding yield on slow annealing, this design also folds rapidly on temperature quenching and dilution from chemical denaturant. This strategy could be used to design folding of other knotted programmable polymers such as RNA or proteins. Objavljeno v DiRROS: 13.04.2016; Ogledov: 5243; Prenosov: 2009
Celotno besedilo (1,70 MB) Gradivo ima več datotek! Več... |