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Szeged-like entropies of graphs
Matthias Dehmer, Frank Emmert-Streib, Niko Tratnik, Petra Žigert Pleteršek, 2022, izvirni znanstveni članek

Ključne besede: Szeged entropy, Mostar entropy, PI entropy, cut method, quotient graphs, sensitivity of a topological descriptor
Objavljeno v DKUM: 20.05.2024; Ogledov: 10; Prenosov: 0
.pdf Celotno besedilo (3,17 MB)
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A method for computing the edge-Hosoya polynomial with application to phenylenes
Martin Knor, Niko Tratnik, 2023, izvirni znanstveni članek

Opis: The edge-Hosoya polynomial of a graph is the edge version of the famous Hosoya polynomial. Therefore, the edge-Hosoya polynomial counts the number of (unordered) pairs of edges at distance $k \ge 0$ in a given graph. It is well known that this polynomial is closely related to the edge-Wiener index and the edge-hyper-Wiener index. As the main result of this paper, we greatly generalize an earlier result by providing a method for calculating the edge-Hosoya polynomial of a graph $G$ which is obtained by identifying two edges of connected bipartite graphs $G_1$ and $G_2$. To show how the main theorem can be used, we apply it to phenylene chains. In particular, we present the recurrence relations and a linear time algorithm for calculating the edge-Hosoya polynomial of any phenylene chain. As a consequence, closed formula for the edge-Hosoya polynomial of linear phenylene chains is derived.
Ključne besede: edge-Hosoya polynomial, graphs, phenylenes
Objavljeno v DKUM: 15.04.2024; Ogledov: 67; Prenosov: 167
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Generalized cut method for computing Szeged-like polynomials with applications to polyphenyls and carbon nanocones
Simon Brezovnik, Niko Tratnik, 2023, izvirni znanstveni članek

Opis: Szeged, Padmakar-Ivan (PI), and Mostar indices are some of the most investigated distance-based Szeged-like topological indices. On the other hand, the polynomials related to these topological indices were also introduced, for example the Szeged polynomial, the edge- Szeged polynomial, the PI polynomial, the Mostar polynomial, etc. In this paper, we introduce a concept of the general Szeged-like polynomial for a connected strength-weighted graph. It turns out that this concept includes all the above mentioned polynomials and also infinitely many other graph polynomials. As the main result of the paper, we prove a cut method which enables us to efficiently calculate a Szeged-like polynomial by using the corresponding polynomials of strength-weighted quotient graphs obtained by a partition of the edge set that is coarser than ▫$\Theta^*$▫-partition. To the best of our knowledge, this represents the first implementation of the famous cut method to graph polynomials. Finally, we show how the deduced cut method can be applied to calculate some Szeged-like polynomials and corresponding topological indices of para-polyphenyl chains and carbon nanocones.
Ključne besede: graph theory, carbon nanocone, topological indices
Objavljeno v DKUM: 25.03.2024; Ogledov: 118; Prenosov: 1
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Izgradnja nove transformatorske postaje Varpolje Kamp Menina : diplomsko delo
Mihael Tratnik, 2024, diplomsko delo

Opis: V diplomskem delu smo se osredotočili na predstavitev, načrtovanje in izdelavo nove transformatorske postaje Varpolje Kamp Menina s priključnim 20 kV kablovodom in nizkonapetostnim kabelskim izvodom. Nova transformatorska postaja se gradi zaradi širitve dejavnosti v Kampu Menina in premajhne razpoložljive priključne moči na že obstoječem nizkonapetostnem kabelskem izvodu ter neekonomičnosti izgradnje nizkonapetostnega kablovoda. S tem bi zagotovili boljše napetostne razmere in več priključne moči za obstoječe in predvidene uporabnike ter izboljšali kakovost oskrbe z električno energijo na tem območju.
Ključne besede: transformatorska postaja, transformator, kablovod, nizka napetost
Objavljeno v DKUM: 18.03.2024; Ogledov: 215; Prenosov: 34
.pdf Celotno besedilo (2,22 MB)

Outerplane bipartite graphs with isomorphic resonance graphs
Simon Brezovnik, Zhongyuan Che, Niko Tratnik, Petra Žigert Pleteršek, 2024, izvirni znanstveni članek

Opis: We present novel results related to isomorphic resonance graphs of 2-connected outerplane bipartite graphs. As the main result, we provide a structure characterization for 2-connected outerplane bipartite graphs with isomorphic resonance graphs. Three additional characterizations are expressed in terms of resonance digraphs, via local structures of inner duals, as well as using distributive lattices on the set of order ideals of posets defined on inner faces of 2-connected outerplane bipartite graphs.
Ključne besede: distributive lattice, inner dual, isomorphic resonance graphs, order ideal, 2-connected outerplane bipartite graph
Objavljeno v DKUM: 29.02.2024; Ogledov: 155; Prenosov: 7
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The multivariable Zhang-Zhang polynomial of phenylenes
Niko Tratnik, 2023, izvirni znanstveni članek

Opis: The Zhang-Zhang polynomial of a benzenoid system is a well-known counting polynomial that was introduced in 1996. It was designed to enumerate Clar covers, which are spanning subgraphs with only hexagons and edges as connected components. In 2018, the generalized Zhang-Zhang polynomial of two variables was defined such that it also takes into account 10-cycles of a benzenoid system. The aim of this paper is to introduce and study a new variation of the Zhang-Zhang polynomial for phenylenes, which are important molecular graphs composed of 6-membered and 4-membered rings. In our case, Clar covers can contain 4-cycles, 6-cycles, 8-cycles, and edges. Since this new polynomial has three variables, we call it the multivariable Zhang-Zhang (MZZ) polynomial. In the main part of the paper, some recursive formulas for calculating the MZZ polynomial from subgraphs of a given phenylene are developed and an algorithm for phenylene chains is deduced. Interestingly, computing the MZZ polynomial of a phenylene chain requires some techniques that are different to those used to calculate the (generalized) Zhang-Zhang polynomial of benzenoid chains. Finally, we prove a result that enables us to find the MZZ polynomial of a phenylene with branched hexagons.
Ključne besede: Zhang-Zhang polynomial, phenylene, Clar cover, Kekulé structure
Objavljeno v DKUM: 09.02.2024; Ogledov: 187; Prenosov: 6
.pdf Celotno besedilo (719,26 KB)
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A new alternative to Szeged, Mostar, and PI polynomials : the SMP polynomials
Martin Knor, Niko Tratnik, 2023, izvirni znanstveni članek

Opis: Szeged-like topological indices are well-studied distance-based molecular descriptors, which include, for example, the (edge-)Szeged index, the (edge-)Mostar index, and the (vertex-)PI index. For these indices, the corresponding polynomials were also defined, i.e., the (edge-)Szeged polynomial, the Mostar polynomial, the PI polynomial, etc. It is well known that, by evaluating the first derivative of such a polynomial at x = 1, we obtain the related topological index. The aim of this paper is to introduce and investigate a new graph polynomial of two variables, which is called the SMP polynomial, such that all three vertex versions of the above-mentioned indices can be easily calculated using this polynomial. Moreover, we also define the edge-SMP polynomial, which is the edge version of the SMP polynomial. Various properties of the new polynomials are studied on some basic families of graphs, extremal problems are considered, and several open problems are stated. Then, we focus on the Cartesian product, and we show how the (edge-)SMP polynomial of the Cartesian product of n graphs can be calculated using the (weighted) SMP polynomials of its factors.
Ključne besede: SMP polynomial, edge-SMP polynomial, Cartesian product, Szeged index, Mostar index, PI index
Objavljeno v DKUM: 09.02.2024; Ogledov: 157; Prenosov: 14
.pdf Celotno besedilo (320,27 KB)
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The use of differential evolution to determine maximum generation and load values in the distribution network
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer, Gorazd Štumberger, Miloš Beković, 2022, izvirni znanstveni članek

Opis: By integrating renewable energy sources into the existing distribution network, the characteristics and local stability of the network is highly impacted. The network, which was built with the goal of a directed energy flow from large conventional sources connected to the transmission network via the distribution network to consumers, can change the direction of the energy flow. The adoption of environmental commitments and directives encourages the integration of local dispersed energy sources, which can worsen voltage conditions in the distribution network. To avoid excessive local production, distribution network operators must limit the installation of new generati on units, as it is necessary to take into account the quality of power supply by monitoring its network parameters, such as the appropriate voltage profi le and the rati o between acti ve and reacti ve power. On the other hand, excessive loads due to the mass transiti on of household heati ng and transport towards electricity can also pose a problem for high-quality electricity supply due to the excessive voltage drop. The arti cle presents an algorithm for determining the maximum size of unit producti on and the maximum load at a node in the distributi on network. Also demonstrated is the use of variable tap transformer technology, which adjusts the tap of the transformer to provide an appropriate voltage profi le in the network. The enti re analysis was performed on a model of a real medium-voltage network, in which solar and hydropower plants are already included. The model was verifi ed by comparing its calculated values with actual measurements. The goal was to determine the size of the unit’s maximum producti on, as well as the size of the maximum load, by using the diff erenti al evoluti on algorithm, while keeping voltage profi les within the permissible limits. The results of the analysis are presented in the article.
Ključne besede: distribution network, renewable energy sources, optimisation method, voltage profile
Objavljeno v DKUM: 30.10.2023; Ogledov: 311; Prenosov: 11
.pdf Celotno besedilo (1,63 MB)
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The possibility of using self-defence against non-state actors : magistrsko delo
Patricija Glavica, 2023, magistrsko delo

Opis: This master’s thesis systematically and in-depth examines the notion of self-defence, primarily through the ratione personae aspect and thus focuses on the possibility of its use against non-state actors. While the use of self-defence against non-state actors is not a new phenomenon in international law, it is nonetheless taking on new dimensions, particularly in the context of the fight against terrorism. The right to self-defence is one of the exceptions to the jus cogens prohibition of the use of force. It is an ‘inherent’ right, codified in Article 51 of the UN Charter and forming part of customary international law. According to the primary understanding, the right to self-defence had a State-centric approach, which was also continuously affirmed in the jurisprudence of the International Court of Justice. Consequently, a State could only use self-defence against a non-state actor if its actions were imputable to another State in whose territory defensive force was being used. However, especially after the 9/11 attack there have been tendencies to broaden the right to self-defence and allow its use even if the actions by a non-state actor are not attributable to a State under the current attributability standards. Due to the complexity of the right to self-defence it requires careful examination through different aspects and sources of international law. It can be observed that the opinions regarding the expansion of the right to self-defence are very different. Firstly, scholars have widely divergent views regarding the correct interpretation of Article 51 of the UN Charter under the rules of the VCLT. Secondly, in its previous judgements, the International Court of Justice has maintained the State-centric approach, while potentially allowing room for a more expansive approach to self-defence. Thirdly, States have since the 9/11 attack started to regularly invoke the right to self-defence when using extraterritorial force against non-state actors. However, the reactions of States relating to such use of force and the opinions of scholars regarding the implications of such State practice, are equivocal. Taking everything into consideration this master’s thesis concludes that neither Article 51 of the UN Charter nor customary international law allow the use of self-defence against non-state actors, whose actions are not attributable to a State. Although the right to self-defence is undoubtedly expanding, its scope is not yet fully crystallized.
Ključne besede: the right to self-defence, non-state actors, the prohibition of the use of force, terrorism, Article 51 of the Charter of the United Nations, extraterritorial use of force, jus ad bellum, Nicaragua case, attributability
Objavljeno v DKUM: 08.09.2023; Ogledov: 608; Prenosov: 104
.pdf Celotno besedilo (1,48 MB)

Katja Ramšak, 2009, diplomsko delo

Opis: Svetovna trgovinska organizacija (WTO) je največja trgovinska organizacija, ki je bila ustanovljena 1. januarja 1995. Njeni temelji so določeni v Splošnem sporazumu o carinah in trgovini (GATT). WTO in izboljšan ter učinkovitejši postopek za reševanje sporov v primerjavi z prejšnjim GATT postopkom je rezultat Urugvajskega kroga pogajanj. Postopek za reševanje sporov v WTO je nadgradnja postopka za reševanje sporov pod GATT sistemom. Pravila, ki urejajo postopek reševanja sporov so urejena v Dogovoru o pravilih in postopkih za reševanje sporov (DSU). Postopek reševanja sporov v WTO poteka v treh fazah. Najprej se postopek začne s posvetovanjem, sledi postopek pred panelno skupino in Pritožbenim organom ter zaključi s izvajanjem poročil panelne skupine in Pritožbenega organa od države kršiteljice. Ko panelna skupina in Pritožbeni organ izdajo poročila, sprejeta od Organa za reševanje sporov, so pravno zavezujoča za države članice.
Ključne besede: Organ za reševanje sporov, Pritožbeni organ, panelna skupina, Dogovor o pravilih in postopkih za reševanje sporov, Splošni sporazum o carinah in trgovini, Mednarodna trgovinska organizacija, Svetovna trgovinska organizacija
Objavljeno v DKUM: 30.08.2023; Ogledov: 324; Prenosov: 13
.pdf Celotno besedilo (869,57 KB)

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