1. Degradation of waste tetra pak packaging with hydrothermal treatment in sub-/supercritical waterMihael Irgolič, Maja Čolnik, Petra Kotnik, Mojca Škerget, 2024, izvirni znanstveni članek Ključne besede: hydrothermal degradation, waste packing, tetra pak, subcritical water, subcritical waste, chemical recycling, one-stage process, two-stage process, product analysis
Objavljeno v DKUM: 16.07.2024; Ogledov: 88; Prenosov: 8
 Celotno besedilo (2,12 MB) |
2. Packings in bipartite prisms and hypercubesBoštjan Brešar, Sandi Klavžar, Douglas F. Rall, 2024, izvirni znanstveni članek Opis: ▫$2$▫-pakirno število ▫$\rho_2(G)$▫ grafa ▫$G$▫ je kardinalnost največjega ▫$2$▫-pakiranja grafa ▫$G$▫, odprto pakirno število ▫$\rho^{\rm o}(G)$▫ pa kardinalnost največjega odprtega pakiranja grafa ▫$G$▫, kjer je odprto pakiranje (oz. ▫$2$▫ pakiranje) množica vozlišč grafa ▫$G$▫, katerih dve (zaprti) soseščini se ne sekata. Dokazano je, da če je ▫$G$▫ dvodelen, potem je ▫$\rho^{\rm o}(G\Box K_2) = 2\rho_2(G)$▫. Za hiperkocke sta določeni spodnji meji ▫$\rho_2(Q_n) \ge 2^{n - \lfloor \log n\rfloor -1}$▫ in ▫$\rho^{\rm o}(Q_n) \ge 2^{n - \lfloor \log (n-1)\rfloor -1}$▫. Te ugotovitve so uporabljene za injektivna barvanja hiperkock. Dokazano je, da je ▫$Q_9$▫ najmanjša hiperkocka, ki ni popolno injektivno obarvljiva. Dokazano je tudi, da je ▫$\gamma_t(Q_{2^k}\times H) = 2^{2^k-k}\gamma_t(H)$▫, kjer je ▫$H$▫ poljuben graf brez izoliranih vozlišč.
Ključne besede: 2-pakirno število, odprto pakirno število, dvodelna prizma, hiperkocke, injektivno barvanje, celotno dominacijsko število, 2-packing number, open packing number, bipartite prism, hypercube, injective coloring, total domination number
Objavljeno v DKUM: 28.02.2024; Ogledov: 260; Prenosov: 5
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3. Incidence dimension and 2-packing number in graphsDragana Božović, Aleksander Kelenc, Iztok Peterin, Ismael G. Yero, 2022, izvirni znanstveni članek Opis: Let ▫$G=(V,E)$▫ be a graph. A set of vertices ▫$A$▫ is an incidence generator for ▫$G$▫ if for any two distinct edges ▫$e,f \in E(G)$▫ there exists a vertex from ▫$A$▫ which is an endpoint of either ▫$e$▫ or ▫$f$▫. The smallest cardinality of an incidence generator for ▫$G$▫ is called the incidence dimension and is denoted by ▫$\dim_I(G)$▫. A set of vertices ▫$P \subseteq V(G)$▫ is a 2-packing of ▫$G$▫ if the distance in ▫$G$▫ between any pair of distinct vertices from ▫$P$▫ is larger than two. The largest cardinality of a 2-packing of ▫$G$▫ is the packing number of ▫$G$▫ and is denoted by ▫$\rho(G)$▫. In this article, the incidence dimension is introduced and studied. The given results show a close relationship between ▫$\dim_I(G)$▫ and ▫$\rho(G)$▫. We first note that the complement of any 2-packing in graph ▫$G$▫ is an incidence generator for ▫$G$▫, and further show that either ▫$\dim_I(G)=|V(G)|-\rho(G)$▫ or ▫$\dim_I(G)=|V(G)-|\rho(G)-1$▫ for any graph ▫$G$▫. In addition, we present some bounds for ▫$\dim_I(G)$▫ and prove that the problem of determining the incidence dimension of a graph is NP-hard.
Ključne besede: incidence dimension, incidence generator, 2-packing
Objavljeno v DKUM: 18.08.2023; Ogledov: 317; Prenosov: 33
Celotno besedilo (434,03 KB)
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4. Orientable domination in product-like graphsSarah Anderson, Boštjan Brešar, Sandi Klavžar, Kirsti Kuenzel, Douglas F. Rall, 2023, izvirni znanstveni članek Opis: The orientable domination number, ▫${\rm DOM}(G)$▫, of a graph ▫$G$▫ is the largest domination number over all orientations of ▫$G$▫. In this paper, ▫${\rm DOM}$▫ is studied on different product graphs and related graph operations. The orientable domination number of arbitrary corona products is determined, while sharp lower and upper bounds are proved for Cartesian and lexicographic products. A result of Chartrand et al. from 1996 is extended by establishing the values of ▫${\rm DOM}(K_{n_1,n_2,n_3})$▫ for arbitrary positive integers ▫$n_1,n_2$▫ and ▫$n_3$▫. While considering the orientable domination number of lexicographic product graphs, we answer in the negative a question concerning domination and packing numbers in acyclic digraphs posed in [Domination in digraphs and their direct and Cartesian products, J. Graph Theory 99 (2022) 359-377].
Ključne besede: digraph, domination, orientable domination number, packing, graph product, corona graph
Objavljeno v DKUM: 09.08.2023; Ogledov: 446; Prenosov: 46
Celotno besedilo (419,38 KB)
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5. Software based encoder/decoder generation for data exchange optimization in the internet of things : master's thesisTjaž Vračko, 2022, magistrsko delo Opis: Efficient encoding of data is an important part of projects in
the Internet of Things space. Communication packets must be kept
as small as possible in order to minimize the power consumption of
devices.
In this thesis, an automatic code generation tool, irpack, is proposed
that will unify the way packets are defined across all future
projects at Institute IRNAS.
Using a schema, this tool generates source code of encoders and
decoders in target programming languages. A schema evolution system
is also defined, by which changes to packets can be compatible
across multiple versions.
The tool is then applied to a selection of past projects to gauge
its usefulness. It is determined that irpack is able to encode the same
data into a similar or smaller size packet, while also providing
additional versioning information.
Ključne besede: encoding/decoding, schema, schema evolution, bit packing, code generation
Objavljeno v DKUM: 31.01.2022; Ogledov: 811; Prenosov: 72
Celotno besedilo (2,58 MB) |
6. Some results on total domination in direct products of graphsPaul Dorbec, Sylvain Gravier, Sandi Klavžar, Simon Špacapan, izvirni znanstveni članek Opis: Upper and lower bounds on the total domination number of the direct product ofgraphs are given. The bounds involve the ▫$\{2\}$▫-total domination number, the total 2-tuple domination number, and the open packing number of the factors. Using these relationships one exact total domination number is obtained. An infinite family of graphs is constructed showing that the bounds are best possible. The domination number of direct products of graphs is also bounded from below.
Ključne besede: mathematics, graph theory, direktni produkt, total domination, ▫$k$▫-tuple domination, open packing, domination
Objavljeno v DKUM: 31.03.2017; Ogledov: 1234; Prenosov: 418
Celotno besedilo (156,67 KB)
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7. On the packing chromatic number of Cartesian products, hexagonal lattice, and treesBoštjan Brešar, Sandi Klavžar, Douglas F. Rall, 2007, izvirni znanstveni članek Opis: Pakirno kromatično število ▫$chi_{rho}(G)$▫ grafa ▫$G$▫ je najmanjše število ▫$k$▫, tako da lahko množico vozlišč grafa ▫$G$▫ razbijemo v pakiranja s paroma različnimi širinami. Dobljenih je več spodnjih in zgornjih meja za pakirno kromatično število kartezičnega produkta grafov. Dokazano je, da pakirno kromatično število šestkotniške mreže leži med 6 in 8. Optimalne spodnje in zgornje meje so dokazane za subdividirane grafe. Obravnavana so tudi drevesa ter vpeljana monotona barvanja.
Ključne besede: matematika, teorija grafov, pakirno kromatično število, kartezični produkt grafov, šestkotniška mreža, subdividiran graf, drevo, računska zahtevnost, mathematics, graph theory, packing chromatic number, Cartesian product of graphs, hexagonal lattice, subdivision graph, tree, computational complexity
Objavljeno v DKUM: 10.07.2015; Ogledov: 1320; Prenosov: 156
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