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1.
Nastavitev MF200 stroja za hladno preoblikovanje in konstruiranje garaže v Vertexu : diplomsko delo
Uroš Brumec, 2022, diplomsko delo

Opis: Na trgu se vedno znova pojavljajo zahteve po znižanju stroškov proizvodnje. Zaradi vedno večje konkurence na trgu smo primorani, da se izdelki v čim večji meri izdelajo znotraj podjetja. V diplomskem delu je predstavljen nov stroj MF200 za hladno preoblikovanje C- in U-profilov v podjetju Hosekra. S programskim paketom Vertex BD, ki se v podjetju uporablja za konstrukcijo izdelkov in programiranje stroja, je izrisano celotno ogrodje garaže. V diplomskem delu je prikazan postopek izrisa in uporabljene funkcije, ki jih podpira stroj pri izdelavi, ter prikazan končen sestavljen izdelek.
Ključne besede: hladno preoblikovanje, preoblikovanje, stroj MF200, C- in U-profili, garaža, Vertex BD
Objavljeno v DKUM: 12.09.2022; Ogledov: 342; Prenosov: 31
.pdf Celotno besedilo (3,26 MB)

2.
K-vertex: a novel model for the cardinality constraints enforcement in graph databases : doctoral dissertation
Martina Šestak, 2022, doktorska disertacija

Opis: The increasing number of network-shaped domains calls for the use of graph database technology, where there are continuous efforts to develop mechanisms to address domain challenges. Relationships as 'first-class citizens' in graph databases can play an important role in studying the structural and behavioural characteristics of the domain. In this dissertation, we focus on studying the cardinality constraints mechanism, which also exploits the edges of the underlying property graph. The results of our literature review indicate an obvious research gap when it comes to concepts and approaches for specifying and representing complex cardinality constraints for graph databases validated in practice. To address this gap, we present a novel and comprehensive approach called the k-vertex cardinality constraints model for enforcing higher-order cardinality constraints rules on edges, which capture domain-related business rules of varying complexity. In our formal k-vertex cardinality constraint concept definition, we go beyond simple patterns formed between two nodes and employ more complex structures such as hypernodes, which consist of nodes connected by edges. We formally introduce the concept of k-vertex cardinality constraints and their properties as well as the property graph-based model used for their representation. Our k-vertex model includes the k-vertex cardinality constraint specification by following a pre-defined syntax followed by a visual representation through a property graph-based data model and a set of algorithms for the implementation of basic operations relevant for working with k-vertex cardinality constraints. In the practical part of the dissertation, we evaluate the applicability of the k-vertex model on use cases by carrying two separate case studies where we present how the model can be implemented on fraud detection and data classification use cases. We build a set of relevant k-vertex cardinality constraints based on real data and explain how each step of our approach is to be done. The results obtained from the case studies prove that the k-vertex model is entirely suitable to represent complex business rules as cardinality constraints and can be used to enforce these cardinality constraints in real-world business scenarios. Next, we analyze the performance efficiency of our model on inserting new edges into graph databases with varying number of edges and outgoing node degree and compare it against the case when there is no cardinality constraints checking. The results of the statistical analysis confirm a stable performance of the k-vertex model on varying datasets when compared against a case with no cardinality constraints checking. The k-vertex model shows no significant performance effect on property graphs with varying complexity and it is able to serve as a cardinality constraints enforcement mechanism without large effects on the database performance.
Ključne besede: Graph database, K-vertex cardinality constraint, Cardinality, Business rule, Property graph data model, Property graph schema, Hypernode, Performance analysis, Fraud detection, Data classification
Objavljeno v DKUM: 10.08.2022; Ogledov: 643; Prenosov: 75
.pdf Celotno besedilo (3,43 MB)

3.
Partitioning the vertex set of ▫$G$▫ to make ▫$G \Box H$▫ an efficient open domination graph
Tadeja Kraner Šumenjak, Iztok Peterin, Douglas F. Rall, Aleksandra Tepeh, 2016, izvirni znanstveni članek

Opis: A graph is an efficient open domination graph if there exists a subset of vertices whose open neighborhoods partition its vertex set. We characterize those graphs ▫$G$▫ for which the Cartesian product ▫$G \Box H$▫ is an efficient open domination graph when ▫$H$▫ is a complete graph of order at least 3 or a complete bipartite graph. The characterization is based on the existence of a certain type of weak partition of ▫$V(G)$▫. For the class of trees when ▫$H$▫ is complete of order at least 3, the characterization is constructive. In addition, a special type of efficient open domination graph is characterized among Cartesian products ▫$G \Box H$▫ when ▫$H$▫ is a 5-cycle or a 4-cycle.
Ključne besede: efficient open domination, Cartesian product, vertex labeling, total domination
Objavljeno v DKUM: 10.07.2017; Ogledov: 1003; Prenosov: 158
.pdf Celotno besedilo (166,60 KB)
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4.
The Hosoya-Wiener polynomial of weighted trees
Blaž Zmazek, Janez Žerovnik, 2007, izvirni znanstveni članek

Opis: Formulas for the Wiener number and the Hosoya-Wiener polynomial of edge and vertex weighted graphs are given in terms of edge and path contributions. For a rooted tree, the Hosoya-Wiener polynomial is expressed as a sum of vertex contributions. Finally, a recursive formula for computing the Hosoya-Wiener polynomial of a weighted tree is given.
Ključne besede: mathematics, graph theory, Hosoya-Wiener polynomial, weighted tree, vertex weighted graphs
Objavljeno v DKUM: 05.07.2017; Ogledov: 1306; Prenosov: 109
.pdf Celotno besedilo (182,69 KB)
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5.
Edge-transitive lexicographic and cartesian products
Wilfried 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 v DKUM: 31.03.2017; Ogledov: 996; Prenosov: 422
.pdf Celotno besedilo (150,33 KB)
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6.
On the vertex k-path cover
Boštjan Brešar, Marko Jakovac, Ján Katrenič, Gabriel Semanišin, Andrej Taranenko, 2013, izvirni znanstveni članek

Opis: A subset ▫$S$▫ of vertices of a graph ▫$G$▫ is called a vertex ▫$k$▫-path cover if every path of order ▫$k$▫ in ▫$G$▫ contains at least one vertex from ▫$S$▫. Denote by ▫$psi_k(G)$▫ the minimum cardinality of a vertex ▫$k$▫-path cover in ▫$G$▫. In this paper, an upper bound for ▫$psi_3$▫ in graphs with a given average degree is presented. A lower bound for ▫$psi_k$▫ of regular graphs is also proven. For grids, i.e. the Cartesian products of two paths, we give an asymptotically tight bound for ▫$psi_k$▫ and the exact value for ▫$psi_3$▫.
Ključne besede: matematika, teorija grafov, vozliščno pokritje, regularni grafi, mreže, mathematics, graph theory, vertex cover, grids
Objavljeno v DKUM: 10.07.2015; Ogledov: 1510; Prenosov: 27
URL Povezava na celotno besedilo

7.
Minimum k-path vertex cover
Boštjan Brešar, František Kardoš, Ján Katrenič, Gabriel Semanišin, 2011, izvirni znanstveni članek

Opis: Podmnožica ▫$S$▫ množice vozlišč grafa ▫$G$▫ se imenuje po poteh ▫$k$▫-vozliščno pokritje, če vsaka pot reda ▫$k$▫ v grafu ▫$G$▫ vsebuje vsaj eno vozlišče iz ▫$S$▫. Označimo s ▫$psi_k(G)$▫ najmanjšo kardinalnost po poteh ▫$k$▫-vozliščnega pokritja v grafu ▫$G$▫. V članku dokažemo, da je problem določitve ▫$psi_k(G)$▫ NP-poln problem za vsak ▫$k geq 2$▫, medtem ko lahko za drevesa ta problem rešimo v linearnem času. Raziskujemo zgornje meje za vrednost ▫$psi_k(G)$▫ in dokažemo več ocen ter točnih vrednosti za to število. Prav tako dokažemo, da je ▫$psi_3(G) leq (2n + m)/6$▫, za vsak graf ▫$G$▫ z ▫$n$▫ vozlišči in ▫$m$▫ povezavami.
Ključne besede: matematika, teorija grafov, algoritem, vozliščno pokritje, pot, NP-polnost, disociacijsko število, po poteh vozliščno pokritje, mathematics, graph theory, algorithm, path, vertex cover, dissociation number, path vertex cover, NP-complete
Objavljeno v DKUM: 10.07.2015; Ogledov: 1173; Prenosov: 20
URL Povezava na celotno besedilo

8.
Transitive, locally finite median graphs with finite blocks
Wilfried Imrich, Sandi Klavžar, 2009, izvirni znanstveni članek

Opis: V članku obravnavamo neskončne, lokalno končne, vozliščno-tranzitivne medianske grafe. Pokazano je, da končnost ▫$Theta$▫-razredov takih grafov ne zagotavlja končnosti blokov. Bloki pa postanejo neskončni, če nadalje nobeno končno zaporedje ▫$Theta$▫-kontrakcij ne naredi novih prereznih vozlišč. Dokazano je, da obstaja končno mnogo vozliščno-tranzitivnih medianskih grafov fiksne stopnje, ki imajo končne bloke. Konstruirana je neskončna družina vozliščno-tranzitivnih medianskih grafov z intranzitivnimi bloki. Podan je tudi seznam vseh vozliščno-tranzitivnih medianskih grafov stopnje 4.
Ključne besede: teorija grafov, medianski grafi, neskočni grafi, vozliščno-tranzitivni grafi, graph theory, median graphs, infinite graphs, vertex-transitive graphs
Objavljeno v DKUM: 10.07.2015; Ogledov: 1524; Prenosov: 101
URL Povezava na celotno besedilo

9.
Transitive, locally finite median graphs with finite blocks
Wilfried Imrich, Sandi Klavžar, 2008

Opis: V članku obravnavamo neskončne, lokalno končne, vozliščno-tranzitivne medianske grafe. Pokazano je, da končnost ▫$Theta$▫-razredov takih grafov ne zagotavlja končnosti blokov. Bloki pa postanejo neskončni, če nadalje nobeno končno zaporedje ▫$Theta$▫-kontrakcij ne naredi novih prereznih vozlišč. Dokazano je, da obstaja končno mnogo vozliščno-tranzitivnih medianskih grafov fiksne stopnje, ki imajo končne bloke. Konstruirana je neskončna družina vozliščno-tranzitivnih medianskih grafov z intranzitivnimi bloki. Podan je tudi seznam vseh vozliščno-tranzitivnih medianskih grafov stopnje 4.
Ključne besede: teorija grafov, medianski grafi, neskočni grafi, vozliščno-tranzitivni grafi, graph theory, median graphs, infinite graphs, vertex-transitive graphs
Objavljeno v DKUM: 10.07.2015; Ogledov: 1620; Prenosov: 94
URL Povezava na celotno besedilo

10.
Maximal proper subgraphs of median graphs
Boštjan Brešar, Sandi Klavžar, 2007, izvirni znanstveni članek

Opis: Za medianski graf ▫$G$▫ in vozlišče ▫$v$▫, ki ni presečno, dokažemo, da je ▫$G-v$▫ medianski graf natanko tedaj, ko ▫$v$▫ ni center dvodelnega kolesa. To je nadalje ekvivalentno obstoju določene eliminacijske sheme za povezave, ki so incidenčne z ▫$v$▫. Rezultat implicira karakterizacijo po vozliščih kritičnih (po vozliščih polnih) medianskih grafov, ki so medianski grafi, katerih vsi podgrafi brez enega vozlišča niso medianski (so medianski). Podani sta tudi dve analogni karakterizaciji za primer odstranjevanja povezav.
Ključne besede: matematika, teorija grafov, medianski graf, podgraf brez enega vozlišča, dvodelno kolo, kvadratna povezava, mathematics, graph theory, median graph, vertex-deleted subgraph, bipartite wheel, square-eddge, square-dismantlable vertex
Objavljeno v DKUM: 10.07.2015; Ogledov: 955; Prenosov: 79
URL Povezava na celotno besedilo

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