1. Integrations on ringsIztok Banič, 2017, izvirni znanstveni članek Opis: In calculus, an indefinite integral of a function f is a differentiable function F whose derivative is equal to f. The main goal of the paper is to generalize this notion of the indefinite integral from the ring of real functions to any ring. We also investigate basic properties of such generalized integrals and compare them to the well-known properties of indefinite integrals of real functions. Ključne besede: ring, integration, Jordan integration, derivation, Jordan derivation Objavljeno: 10.05.2017; Ogledov: 12; Prenosov: 0 Polno besedilo (234,00 KB) |
2. How long can one bluff in the domination game?Boštjan Brešar, Paul Dorbec, Sandi Klavžar, Gašper Košmrlj, 2017, izvirni znanstveni članek Opis: The domination game is played on an arbitrary graph ▫$G$▫ by two players, Dominator and Staller. The game is called Game 1 when Dominator starts it, and Game 2 otherwise. In this paper bluff graphs are introduced as the graphs in which every vertex is an optimal start vertex in Game 1 as well as in Game 2. It is proved that every minus graph (a graph in which Game 2 finishes faster than Game 1) is a bluff graph. A non-trivial infinite family of minus (and hence bluff) graphs is established. Minus graphs with game domination number equal to 3 are characterized. Double bluff graphs are also introduced and it is proved that Kneser graphs ▫$K(n,2)$▫, za ▫$n \ge 6$▫, are double bluff. The domination game is also studied on generalized Petersen graphs and on Hamming graphs. Several generalized Petersen graphs that are bluff graphs but not vertex-transitive are found. It is proved that Hamming graphs are not double bluff. Ključne besede: domination game, game domination number, bluff graphs, minus graphs, generalized Petersen graphs, Kneser graphs, Cartesian product of graphs, Hamming graphs Objavljeno: 09.05.2017; Ogledov: 23; Prenosov: 2 Polno besedilo (56,60 KB) |
3. High potential of sub-Mediterranean dry grasslands for sheep epizoochoryMitja Kaligarič, Jožica Brecl, Sonja Škornik, 2016, izvirni znanstveni članek Opis: There is a general decline of grasslands across Europe due to habitat loss and degradation. Ensuring plant dispersal thus becomes a key process for preserving grassland patches in all scales. We examined diaspore dispersal by sheep epizoochory in the pastures of the North Adriatic Karst (NW Slovenia) and determined the qualitative and quantitative features of diaspores in fur. We recorded 25,650 diaspores of 141 plant taxa (with 107 taxa and 23,350 diaspores determined to species level), using three different methods: (i) the “whole-coat method”, (ii) the “part-of-thecoat method” and (iii) a “seedling emergence method”. A comparison of these techniques revealed that the “wholecoat method” provided the highest number of diaspores and plant species. All diaspores were clustered into five emergent groups based on seven functional traits (diaspore weight, length, width, height, volume, specific weight and the diaspore surface structure). Our research revealed that sheep represent an important dispersal vector, since about half of the plant species recorded in the pastures were found as diaspores in fur. This study contributes to knowledge about the modes of seed dispersal in seminatural grasslands. Taking into account that livestock play a key role in vegetation dynamics, understanding their effects on seed dispersal is essential for conservation and restoration of these species-rich grassland communities. Ključne besede: community assembly, diaspore traits, plant dispersal, seedling emergence method, transhumance Objavljeno: 03.04.2017; Ogledov: 45; Prenosov: 0 Polno besedilo (173,31 KB) |
4. The periphery graph of a median graphBoštjan Brešar, Manoj Changat, Ajitha R. Subhamathi, Aleksandra Tepeh, 2010, izvirni znanstveni članek Opis: The periphery graph of a median graph is the intersection graph of its peripheral subgraphs. We show that every graph without a universal vertex can be realized as the periphery graph of a median graph. We characterize those median graphs whose periphery graph is the join of two graphs and show that they are precisely Cartesian products of median graphs. Path-like median graphs are introduced as the graphs whose periphery graph has independence number 2, and it is proved that there are path-like median graphs with arbitrarily large geodetic number. Peripheral expansion with respect to periphery graph is also considered, and connections with the concept of crossing graph are established. Ključne besede: mathematics, graph theory, median graph, Cartesian product, geodesic, periphery, peripheral expansion Objavljeno: 31.03.2017; Ogledov: 77; Prenosov: 0 Polno besedilo (145,86 KB) |
5. |
6. On [Theta]-graphs of partial cubesSandi Klavžar, Matjaž Kovše, 2007, izvirni znanstveni članek Opis: The ▫$\Theta$▫-graph ▫$\Theta(G)$▫ of a partial cube ▫$G$▫ is the intersection graph of the equivalence classes of the Djokovic-Winkler relation. ▫$\Theta$▫-graphs that are 2-connected, trees, or complete graphs are characterized. In particular, ▫$\Theta(G)$▫ is complete if and only if ▫$G$▫ can be obtained from ▫$K_1$▫ by a sequence of (newly introduced) dense expansions. ▫$\Theta$▫-graphs are also compared with familiar concepts of crossing graphs and ▫$\tau$▫-graphs. Ključne besede: mathematics, graph theory, intersection graph, partial cube, median graph, expansion theorem, Cartesian product of graphs Objavljeno: 31.03.2017; Ogledov: 33; Prenosov: 1 Polno besedilo (150,56 KB) |
7. Edge-transitive lexicographic and cartesian productsWilfried Imrich, Ali Iranmanesh, Sandi Klavžar, Abolghasem Soltani, 2016, izvirni znanstveni članek Opis: In this note connected, edge-transitive lexicographic and Cartesian products are characterized. For the lexicographic product ▫$G \circ H$▫ of a connected graph ▫$G$▫ that is not complete by a graph ▫$H$▫, we show that it is edge-transitive if and only if ▫$G$▫ is edge-transitive and ▫$H$▫ is edgeless. If the first factor of ▫$G \circ H$▫ is non-trivial and complete, then ▫$G \circ H$▫ is edge-transitive if and only if ▫$H$▫ is the lexicographic product of a complete graph by an edgeless graph. This fixes an error of Li, Wang, Xu, and Zhao (Appl. Math. Lett. 24 (2011) 1924--1926). For the Cartesian product it is shown that every connected Cartesian product of at least two non-trivial factors is edge-transitive if and only if it is the Cartesian power of a connected, edge- and vertex-transitive graph. Ključne besede: edge-transitive graph, vertex-transitive graph, lexicographic product of graphs, Cartesian product of graphs Objavljeno: 31.03.2017; Ogledov: 42; Prenosov: 1 Polno besedilo (150,33 KB) |
8. Domination game critical graphsCsilla Bujtás, Sandi Klavžar, Gašper Košmrlj, izvirni znanstveni članek Opis: The domination game is played on a graph ▫$G$▫ by two players who alternately take turns by choosing a vertex such that in each turn at least one previously undominated vertex is dominated. The game is over when each vertex becomes dominated. One of the players, namely Dominator, wants to finish the game as soon as possible, while the other one wants to delay the end. The number of turns when Dominator starts the game on ▫$G$▫ and both players play optimally is the graph invariant ▫$\gamma_g(G)$▫, named the game domination number. Here we study the ▫$\gamma_g$▫-critical graphs which are critical with respect to vertex predomination. Besides proving some general properties, we characterize ▫$\gamma_g$▫-critical graphs with ▫$\gamma_g =2$▫ and with ▫$\gamma_g =3$▫, moreover for each ▫$n$▫ we identify the (infinite) class of all ▫$\gamma_g$▫-critical ones among the ▫$n$▫th powers ▫$C_N^n$▫ of cycles. Along the way we determine ▫$\gamma_g(C_N^n)$▫ for all ▫$n$▫ and ▫$N$▫. Results of a computer search for ▫$\gamma_g$▫-critical trees are presented and several problems and research directions are also listed. Ključne besede: domination game, domination game critical graphs, powers of cycles, trees Objavljeno: 31.03.2017; Ogledov: 38; Prenosov: 0 Polno besedilo (194,74 KB) |
9. 1-factors and characterization of reducible faces of plane elementary bipartite graphsAndrej Taranenko, Aleksander Vesel, 2012, izvirni znanstveni članek Opis: As a general case of molecular graphs of benzenoid hydrocarbons, we study plane bipartite graphs with Kekulé structures (1-factors). A bipartite graph ▫$G$▫ is called elementary if ▫$G$▫ is connected and every edge belongs to a 1-factor of ▫$G$▫. Some properties of the minimal and the maximal 1-factor of a plane elementary graph are given. A peripheral face ▫$f$▫ of a plane elementary graph is reducible, if the removal of the internal vertices and edges of the path that is the intersection of ▫$f$▫ and the outer cycle of ▫$G$▫ results in an elementary graph. We characterize the reducible faces of a plane elementary bipartite graph. This result generalizes the characterization of reducible faces of an elementary benzenoid graph. Ključne besede: mathematics, graph theory, plane elementary bipartite graph, reducible face, benzenoid graph Objavljeno: 31.03.2017; Ogledov: 36; Prenosov: 0 Polno besedilo (139,73 KB) |
10. On derivations of operator algebras with involutionNejc Širovnik, Joso Vukman, 2014, izvirni znanstveni članek Opis: The purpose of this paper is to prove the following result. Let X be a complex Hilbert space, let L(X) be an algebra of all bounded linear operators on X and let A(X) ⊂ L(X) be a standard operator algebra, which is closed under the adjoint operation. Suppose there exists a linear mapping D : A(X) → L(X) satisfying the relation 2D(AA*A) = D(AA*)A + AA*D(A) + D(A)A*A + AD(A*A) for all A ∈ A(X). In this case, D is of the form D(A) = [A,B] for all A ∈ A(X) and some fixed B ∈ L(X), which means that D is a derivation. Ključne besede: mathematics, prime rings, semiprime rings, derivation, Jordan derivation, Banach space Objavljeno: 31.03.2017; Ogledov: 34; Prenosov: 0 Polno besedilo (343,43 KB) |