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1.
Incidence dimension and 2-packing number in graphs
Dragana 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: 159; Prenosov: 11
.pdf Celotno besedilo (434,03 KB)
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2.
Orientable domination in product-like graphs
Sarah 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: 274; Prenosov: 18
.pdf Celotno besedilo (419,38 KB)
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3.
Software based encoder/decoder generation for data exchange optimization in the internet of things : master's thesis
Tjaž 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: 613; Prenosov: 61
.pdf Celotno besedilo (2,58 MB)

4.
Some results on total domination in direct products of graphs
Paul 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: 1088; Prenosov: 399
.pdf Celotno besedilo (156,67 KB)
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5.
On the packing chromatic number of Cartesian products, hexagonal lattice, and trees
Boštjan 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: 1156; Prenosov: 153
URL Povezava na celotno besedilo

6.
On the Leech-Conway sphere packing in S [sup] ([infinity]) space
Leila Marek-Crnjac, 2002, izvirni znanstveni članek

Opis: Ocenimo dimenzijo glavne sfere v neskončno dimenzionalnem prostoru, pri čemer bomo uporabili Leech-Conwayevo mrežo. Numerični rezultati so izpopolnili El Naschiejeve izračune (Chaos, Solitons and Fractals 9 (8) 1998; 1445-1471) in so potrdili štiridimenzionalnost pričakovane sfere.
Ključne besede: sferna napolnitev, Leech-Conwayeva mreža, Leech-Conway lattice, sphere packing
Objavljeno v DKUM: 10.07.2015; Ogledov: 830; Prenosov: 33
URL Povezava na celotno besedilo

7.
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