1. The importance of labeling products with a GMO or non-GMO labelKatja Meško Kuralt, 2021, original scientific article Abstract: The article is based on publicly available data, namely on European legislation and on publicly available instructions or recommendations/guidelines dealing with the field of GMO labelling in Slovenia. The importance of labelling GMO-free products and GMO-labelled products was analysed using a comparative research method. The analysis is based on a comparison of the basic terms with each other (i.e., GMO-labelled products, non-GMO-labelled products). It also is based on a review of the legal definition of the terms and on control over the use of the terms. The purpose of this paper is to define an important difference between the two concepts, which are hidden and (or) not defined for most consumers.
Keywords: GMO label, transparency, product control, product approval process, Regulation 1830/2003/EC
Published in DKUM: 24.09.2024; Views: 0; Downloads: 5
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2. An asymptotic relation between the wirelength of an embedding and the Wiener indexK. Jagadeesh Kumar, Sandi Klavžar, R. Sundara Rajan, Indra Rajasingh, T. M. Rajalaxmi, 2021, original scientific article Abstract: Wirelength is an important criterion to validate the quality of an embedding of a graph into a host graph and is used in particular in VLSI (Very-Large-Scale Integration) layout designs. Wiener index plays a significant role in mathematical chemistry, cheminformatics, and elsewhere. In this note these two concepts are related by proving that the Wiener index of a host graph is an upper bound for the wirelength of a given embedding. The wirelength of embedding complete ▫$2^p$▫-partite graphs into Cartesian products of paths and/or cycles as the function of the Wiener index is determined. The result is an asymptotic approximation of the general upper bound.
Keywords: Wiener index, embedding, wirelength, complete 2p-partite graph, Cartesian product of graphs, integer labeling
Published in DKUM: 23.09.2024; Views: 0; Downloads: 1
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3. On general position sets in Cartesian productsSandi Klavžar, Balázs Patkós, Gregor Rus, Ismael G. Yero, 2021, original scientific article Abstract: The general position number gp(G) of a connected graph G is the cardinality of a largest set S of vertices such that no three distinct vertices from S lie on a common geodesic; such sets are refereed to as gp-sets of G. The general position number of cylinders Pr ◻ Cs is deduced. It is proved that (Cr ◻ Cs)∈{6,7} whenever r ≥ s ≥ 3, s ≠ 4, and r ≥ 6. A probabilistic lower bound on the general position number of Cartesian graph powers is achieved. Along the way a formula for the number of gp-sets in Pr ◻ Ps, where r,s ≥ 2, is also determined.
Keywords: general position problem, Cartesian product of graphs, paths and cycles, probabilistic constructions, exact enumeration
Published in DKUM: 27.08.2024; Views: 39; Downloads: 7
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5. Mutual-visibility sets in cartesian products of paths and cyclesDanilo Korže, Aleksander Vesel, 2024, original scientific article Abstract: For a given graph G, the mutual-visibility problem asks for the largest set of vertices M ⊆ V (G) with the property that for any pair of vertices u, v ∈ M there exists a shortest u, v-path of G that does not pass through any other vertex in M. The mutual-visibility problem for Cartesian products of a cycle and a path, as well as for Cartesian products of two cycles, is considered. Optimal solutions are provided for the majority of Cartesian products of a cycle and a path, while for the other family of graphs, the problem is completely solved.
Keywords: mutual-visibility set, supermutual-visibility number, Cartesian product
Published in DKUM: 14.08.2024; Views: 73; Downloads: 5
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6. A new framework to approach Vizing's conjectureBoštjan Brešar, Bert L. Hartnell, Michael A. Henning, Kirsti Kuenzel, Douglas F. Rall, 2021, original scientific article Abstract: We introduce a new setting for dealing with the problem of the domination number of the Cartesian product of graphs related to Vizing's conjecture. The new framework unifies two different approaches to the conjecture. The most common approach restricts one of the factors of the product to some class of graphs and proves the inequality of the conjecture then holds when the other factor is any graph. The other approach utilizes the so-called Clark-Suen partition for proving a weaker inequality that holds for all pairs of graphs. We demonstrate the strength of our framework by improving the bound of Clark and Suen as follows: ɣ(X◻Y) ≥ max{1/2ɣ(X) ɣt(Y), 1/2ɣt(X) ɣ(Y)}, where ɣ stands for the domination number, ɣt is the total domination number, and X◻Y is the Cartesian product of graphs X and Y.
Keywords: Cartesian product, total domination, Vizing's conjecture, Clark and Suen bound
Published in DKUM: 09.08.2024; Views: 86; Downloads: 8
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7. On Grundy total domination number in product graphsBoštjan Brešar, Csilla Bujtás, Tanja Dravec, Sandi Klavžar, Gašper Košmrlj, Tilen Marc, Balázs Patkós, Zsolt Tuza, Máté Vizer, 2021, original scientific article Abstract: A longest sequence (v1,....,vk) of vertices of a graph G is a Grundy total dominating sequence of G if for all i, N(vi)\U{j=1}^{i-1} N(vj)≠∅. The length k of the sequence is called the Grundy total domination number of G and denoted ɣ{gr}^{t}(G). In this paper, the Grundy total domination number is studied on four standard graph products. For the direct product we show that ɣ{gr}^{t}(G x H) > ɣ{gr}^{t}(G)ɣ{gr}^{t}(H), conjecture that the equality always holds, and prove the conjecture in several special cases. For the lexicographic product we express ɣ{gr}^{t}(G o H) in terms of related invariant of the factors and find some explicit formulas for it. For the strong product, lower bounds on ɣ{gr}^{t}(G ⊠ H) are proved as well as upper bounds for products of paths and cycles. For the Cartesian product we prove lower and upper bounds on the Grundy total domination number when factors are paths or cycles.
Keywords: total domination, Grundy total domination number, graph product
Published in DKUM: 07.08.2024; Views: 96; Downloads: 9
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8. Degradation of waste tetra pak packaging with hydrothermal treatment in sub-/supercritical waterMihael Irgolič, Maja Čolnik, Petra Kotnik, Mojca Škerget, 2024, original scientific article Keywords: hydrothermal degradation, waste packing, tetra pak, subcritical water, subcritical waste, chemical recycling, one-stage process, two-stage process, product analysis
Published in DKUM: 16.07.2024; Views: 88; Downloads: 8
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9. Distance formula for direct-co-direct product in the case of disconnected factorsAleksander Kelenc, Iztok Peterin, 2023, original scientific article Abstract: Direktni-ko-direktni produkt ▫$G\circledast H$▫ grafov ▫$G$▫ in ▫$H$▫ je graf na množizi vozlišč ▫$V(G)\times V(H)$▫. Vozlišči ▫$(g,h)$▫ in ▫$(g',h')$▫ sta sosednji, če je ▫$gg'\in E(G)$▫ in ▫$hh'\in E(H)$▫ ali ▫$gg'\notin E(G)$▫ in ▫$hh'\notin E(H)$▫. Naj bo največ eden izmed faktorjev ▫$G$▫ in ▫$H$▫ povezan. Pokažemo da je razdalja med dvema vozliščema v ▫$G\circledast H$▫ omejena s tri, razen v majhnem številu izjem. Vse izjeme so natančno popisane, kar prinese razdaljno formulo za ▫$G\circledast H$▫.
Keywords: direktni-ko-direktni produkt, razdalja, ekscentričnost, nepovezan graf, direct-co-direct product, distance, eccentricity, disconnected graphs
Published in DKUM: 21.05.2024; Views: 115; Downloads: 6
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10. The essential facilities doctrine, intellectual property rights, and access to big dataRok Dacar, 2023, original scientific article Abstract: This paper analyzes the criteria for applying the essential facilities doctrine to intellectual property rights and the possibility of applying it in cases where Big Data is the alleged essential facility. It aims to answer the research question: ‘‘What are the specifics of the intellectual property criteria in essential facilities cases and are these criteria applicable to Big Data?’’ It points to the semantic openness of the ‘‘new product’’ and ‘‘technical progress’’ conditions that have been developed for assessing whether an intellectual property right constitutes an essential facility. The paper argues that the intellectual property criteria are not applicable in all access to Big Data cases because Big Data is not necessarily protected by copyright. While a set of Big Data could be protected by copyright if certain conditions are met, even in such cases the lack of intrinsic value of Big Data significantly limits the applicability of the intellectual property criteria.
Keywords: essential facilities doctrine, intellectual property rights, big data, new product condition, technical progress condition
Published in DKUM: 11.04.2024; Views: 224; Downloads: 18
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