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21.
22.
Distinguishing Cartesian powers of graphs
Wilfried Imrich, Sandi Klavžar, 2006, original scientific article

Abstract: Razlikovalno število ▫$D(G)$▫ grafa je najmanjše celo število ▫$d$▫, za katero obstaja taka ▫$d$▫-označitev točk grafa ▫$G$▫, da je ne ohranja noben avtomorfizem grafa ▫$G$▫. Dokažemo, da je razlikovalno število kvadrata in višjih potenc povezanega grafa ▫$G ne K_2, K_3$▫, glede na kartezični produkt, vedno enako 2. Ta rezultat je močnejši od rezultatov Albertsona [Electron J Combin, 12 (2005), N17] za potence pra-grafov in tudi od rezultatov Klavžarja and Zhuja [European J. Combin, v tisku]. Bolj splošno, dokažemo tudi, da je ▫$(G Box H) = 2$▫, če sta ▫$G$▫ in ▫$H$▫ relativno tuja grafa in je ▫$|H| le |G| < 2^{|H|} - |H|$▫. Pod podobnimi pogoji veljajo sorodni rezultati tudi za potence grafov glede na krepki in direktni produkt grafov.
Keywords: matematika, teorija grafov, razlikovalno število, grafovski avtomorfizem, produkti grafov, mathematics, graph theory, distingushing number, graph automorphism, products of graphs
Published: 10.07.2015; Views: 370; Downloads: 52
URL Link to full text

23.
Cartesian powers of graphs can be distinguished by two labels
Sandi Klavžar, Xuding Zhu, 2007, original scientific article

Abstract: The distinguishing number ▫$D(G)$▫ of a graph ▫$G$▫ is the least integer ▫$d$▫ such that there is a ▫$d$▫-labeling of the vertices of ▫$G$▫ which is not preserved by any nontrivial automorphism. For a graph ▫$G$▫ let ▫$G^r$▫ be the ▫$r$▫-th power of ▫$G$▫ with respect to the Cartesian product. It is proved that ▫$D(G^r) = 2$▫ for any connected graph ▫$G$▫ with at least 3 vertices and for any ▫$r = 3$▫. This confirms and strengthens a conjecture of Albertson. Other graph products are also considered and a refinement of the Russell and Sundaram motion lemma is proved.
Keywords: matematika, teorija grafov, razlikovalno število, grafovski avtomorfizem, produkti grafov, mathematics, graph theory, distingushing number, graph automorphism, products of graphs
Published: 10.07.2015; Views: 377; Downloads: 52
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24.
Cancellation properties of products of graphs
Wilfried Imrich, Sandi Klavžar, Douglas F. Rall, 2007, short scientific article

Abstract: V tem kratkem prispevku razširimo rezultate Fernándeza, Leightona in López-Presa o enoličnosti ▫$r$▫-tih korenov nepovezanih grafov glede na kartezični produkt na druge produkte in pokažemo, da lahko z njihovimi metodami izpeljemo nova pravila krajšanja.
Keywords: matematika, teorija grafov, produkti grafov, pravilo krajšanja, enoličnost korenov, mathematics, graph theory, graph products, cancellation property, uniqueness of roots
Published: 10.07.2015; Views: 419; Downloads: 54
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25.
Distance-balanced graphs
Janja Jerebic, Sandi Klavžar, Douglas F. Rall, 2008, original scientific article

Abstract: V članku so vpeljani razdaljno uravnoteženi grafi kot grafi, v katerih ima vsaka povezava ▫$uv$▫ naslednjo lastnost: število točk, ki so bližje ▫$u$▫ kot ▫$v$▫, je enako kot število točk, ki so bližje ▫$v$▫ kot ▫$u$▫. Dobljene so osnovne lastnosti teh grafov. Novi koncept je povezan z grafovskimi simetrijami, študirane so tudi lokalne operacije na grafih glede na razdaljno uravnoteženost. Karakterizirani so razdaljno uravnoteženi kartezični in leksikografski produkti grafov. Postavljenih je več odprtih problemov.
Keywords: matematika, teorija grafov, razdalja, razdaljno uravnoteženi grafi, produkti grafov, povezanost, mathematics, graph theory, graph distance, distance-balanced graphs, graph products, connectivity
Published: 10.07.2015; Views: 462; Downloads: 61
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26.
The edge fault-diameter of Cartesian graph bundles
Iztok Banič, Rija Erveš, Janez Žerovnik, 2009, original scientific article

Abstract: Kartezični svežnji so posplošitev krovnih grafov in kartezičnih grafovskih produktov. Naj bo ▫$G$▫ nek s povezavami ▫$k_G$▫-povezan graf in ▫${bar{mathcal{D}}_c(G)}$▫ največji premer podgrafov grafa ▫$G$▫ dobljenih z odstranitvijo $▫c < k_G$▫ povezav. Dokazano je, da je ▫${bar{mathcal{D}}_{a+b+1}(G)} le {bar{mathcal{D}}_a(F)} le {bar{mathcal{D}}_b(B)} + 1$▫, če je ▫$G$▫ grafovski sveženj z vlaknom ▫$F$▫ in bazo ▫$B$▫, ▫$a < k_F$▫, ▫$b < k_B▫$. Dokazano je tudi, da je povezanost s povezavami grafovskega svežnja ▫$G▫$ vsaj ▫$k_F + k_B$▫.
Keywords: matematika, teorija grafov, kartezični grafovski produkti, kartezični grafovski svežnji, povezavni okvarni premer, mathematics, graph theory, Cartesian graph products, Cartesian graph bundles, edge-fault diameter
Published: 10.07.2015; Views: 544; Downloads: 55
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27.
Atoms and clique separators in graph products
Bijo S. Anand, Kannan Balakrishnan, Manoj Changat, Iztok Peterin, 2012, original scientific article

Abstract: Predstavljeni so vsi minimalni klični separatorji za vse štiri standardne produkte: kartezičnega, krepkega, leksikografskega in direktnega. Maksimalne atome natančno opišemo le za prve tri prej omenjene standardne produkte. V direktnem produktu maksimalne atome opišemo le delno. Tipična situacija za standardni grafovski produkt je, da ne vsebuje kličnih separatorjev in je posledično ves produkt maksimalni atom.
Keywords: matematika, teorija grafov, produkt grafov, klični separator, atom, mathematics, graph theory, clique separator, atom, graph products
Published: 10.07.2015; Views: 347; Downloads: 66
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28.
Commercial aquaponics approaching the European market: to consumers' perceptions of aquaponics products in Europe
Vesna Miličić, Ragnheidur Thorarinsdottir, Maria Dos Santos, Maja Turnšek, 2017, original scientific article

Abstract: The first commercial aquaponics companies are starting up in Europe. The main focus has been on solving technology issues and optimizing production. However, increasing attention is now being paid to certification and regulations linked to aquaponics, as well as the marketing of products and services. The paper presents the results of a study whose main aim was to estimate consumers’ knowledge about aquaponics and their acceptance of aquaponics products in different European regions. An on-line questionnaire was administered to the general public through the aquaponics network of Food and Agriculture COST (European Cooperation in Science and Technology) Action FA1305 “The EU Aquaponics Hub—Realising Sustainable Integrated Fish and Vegetable Production for the EU” in 16 European countries. The methodology includes univariate and multivariate statistical techniques. The results show that, on average, attitudes towards aquaponics were positive, showing no significant differences between those who already knew about aquaponics and those who only heard about it through the survey. More than 50% of respondents had never heard of aquaponics, whilst more than 70% had already heard of hydroponics. No more than 17% of respondents were willing to pay more for aquaponically produced products and no more than 40% more when compared to the price of products from conventional farming. The results confirm three different clusters of potential consumers of aquaponics products. They also suggest an urgent need for implementing integrated and holistic approaches involving all stakeholders in aquaponics, in order to define a marketing plan and efficient communication strategies. This COST action, other projects and public decision makers must invest in educating consumers about aquaponics through the organization of guided tours, thematic workshops and tastings of aquaponics products in order to raise their awareness about this new technology. It is absolutely urgent that public decision makers, in cooperation with aquaponics stakeholders, address the main institutional constraints, namely the introduction of aquaponics as an economic activity and the organic certification of aquaponics products.
Keywords: aquaponics, hydroponics, aquaponics products, consumers' acceptance, questionnaire, multivariate statistics, Europe
Published: 22.06.2017; Views: 486; Downloads: 220
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29.
Multi-criteria and econometric evaluation of dairy products
Karmen Pažek, Jernej Turk, Sebjan Hari, Črtomir Rozman, Jernej Prišenk, 2014, original scientific article

Abstract: This study examined the multi-criteria assessment of four dairy products: "Pomursko mlejko" (Pomurje milk), "Lejko mleko" (light milk), "Fyto mleko" (Fyto milk) and "Posneto mleko v prahu" (dried milk). The research was executed by using a multi-criteria methodology, DEX, which was complemented by an econometric analysis for light milk to estimate the trends in production and consumption before analyzed dairy products were implemented on the market. DEXi computer program results indicated that all analyzed milk products were 'above average'. The econometric model was applied to examine changes in the demand for low-fat milk (light milk). Empirical results showed significant consumer response to the increase in the prices of low-fat milk demonstrating income elasticity (1,15 unit).
Keywords: multi-attribute decision theory, DEXi, econometric analysis, milk products
Published: 10.07.2017; Views: 403; Downloads: 57
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30.
Efficient open domination in graph products
Dorota Kuziak, Iztok Peterin, Ismael G. Yero, 2014, original scientific article

Abstract: A graph ▫$G$▫ is an efficient open domination graph if there exists a subset ▫$D$▫ of ▫$V(G)$▫ for which the open neighborhoods centered in vertices of ▫$D$▫ form a partition of ▫$V(G)$▫. We completely describe efficient open domination graphs among lexicographic, strong, and disjunctive products of graphs. For the Cartesian product we give a characterization when one factor is ▫$K_2$▫.
Keywords: graph theory, efficient open domination, graph products, total domination
Published: 10.07.2017; Views: 307; Downloads: 45
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