1. Redox state is similar in subjects following omnivorous, vegan, vegetarian, and low-carbohydrate high-fat dietNives Bogataj Jontez, Karin Šik Novak, Zala Jenko Pražnikar, Ana Petelin, Nina Mohorko, Saša Kenig, 2025, original scientific article Abstract: Age-related noncommunicable diseases are a major health burden in developed countries, with oxidative stress being a key contributing factor. This cross-sectional study aimed to test the hypothesis that redox status among 88 participants with a particular interest in nutrition and habitually following 4 popular dietary patterns (vegan, vegetarian, low-carbohydrate high-fat, and omnivorous), is similar, but correlates with diet quality. Dietary intake was assessed using food diaries, and venous blood samples were collected to measure serum total antioxidative capacity (TAC), bilirubin, nicotinamide adenine dinucleotide (NAD⁺)/reduced form of nicotinamide adenine dinucleotide (NADH) ratio, and sirtuin 1 concentration, and the expression of antioxidative enzymes in leukocytes. TAC and the NAD⁺/NADH ratio were higher in the vegan group compared with the vegetarian group, whereas bilirubin concentration was higher in the omnivorous compared with the low-carbohydrate high-fat group. Other differences between the dietary groups were not significant. NAD+/NADH ratio and sirtuin 1 were positively correlated with diet quality, assessed with the Healthy Eating Index. Correlation analysis between dietary variables and redox markers revealed only a few weak to moderate associations. However, a hierarchical regression model including age, gender, and dietary variables explained 19.8% of the variance in TAC, 21.2% of the variance in the NAD⁺/NADH ratio, and 44.3% of the variance in sirtuin 1 concentration. Therefore, in healthy, relatively young participants with appropriate energy intakes, endogenous mechanisms are able to compensate for oxidative stress to a similar extent, regardless of dietary pattern. Nonetheless, overall diet quality and food selection appear to play a meaningful role in redox balance.
Keywords: oxidative stress, total antioxidative capacity, sirtuin 1, diet quality
Published in RUP: 02.12.2025; Views: 292; Downloads: 2
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2. A sharp upper bound for the harmonious total chromatic number of graphs and multigraphsMarién Abreu, John Baptist Gauci, Davide Mattiolo, Giuseppe Mazzuoccolo, Federico Romaniello, Christian Rubio-Montiel, Tommaso Traetta, 2025, original scientific article Abstract: A proper total colouring of a graph G is called harmonious if it has the further property that when replacing each unordered pair of incident vertices and edgeswith their colours, then no pair of colours appears twice. The smallest number of colours for it to exist is called the harmonious total chromatic number of G, denoted by h_t(G). Here, we give a general upper bound for h_t(G) in terms of the order n of G. Our two main results are obvious consequences of the computation of the harmonious total chromatic number of the complete graph Kn and of the complete multigraph λK_n, where λ is the number of edges joining each pair of vertices of Kn. In particular, Araujo-Pardo et al. have recently shown that 3/2 n ≤ h_t(K_n)≤ 5/3 n + θ(1). In this paper, we prove that h_t(K_n) = ⌈3/2 n⌉ except for h_t(K₁) = 1 and h_t(K₄) = 7; therefore, h_t(G)≤ ⌈3/2 n⌉, for every graph G on n > 4 vertices. Finally, we extend such a result to the harmonious total chromatic number of the complete multigraph λKn and as a consequence show that h_t(G) ≤ (λ-1)(2⌈n/2⌉-1)+⌈3n/2⌉ for n > 4, where G is a multigraph such that λ is the maximum number of edges between any two vertices.
Keywords: total colouring, harmonious colouring, complete graphs, complete multigraphs, Levi graph
Published in RUP: 03.11.2025; Views: 335; Downloads: 5
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3. Brooks' type theorems for coloring parameters of locally finite graphs and Kőnig's LemmaAmitayu Banerjee, Zalán Molnár, Alexa Gopaulsingh, 2025, original scientific article Abstract: In the past, analogues to Brooks’ theorem have been found for various parameters of graph coloring for infinite locally finite connected graphs in ZFC. We prove that there is a model of ZF (i.e., the Zermelo–Fraenkel set theory without the Axiom of Choice (AC)) where these theorems fail. Moreover, such theorems follow from Kőnig’s Lemma (every infinite locally finite connected graph has a ray–a weak form of AC) in ZF. In ZF, inspired by a combinatorial argument of Herrlich and Tachtsis from 2006, we formulate new conditions for the existence of the distinguishing chromatic number, the distinguishing chromatic index, the total chromatic number, the total distinguishing chromatic number, the odd chromatic number, and the neighbor-distinguishing index in infinite locally finite connected graphs, which are equivalent to Kőnig’s Lemma.
In this direction, we strengthen a recent result of Stawiski from 2023. We also generalize an algorithm of Imrich, Kalinowski, Pilśniak, and Shekarriz to show that the statement “If G is a connected infinite graph where the maximum degree Δ(G) ≥ 3 is finite, then the list-distinguishing chromatic number is at most 2Δ(G) − 1” holds under Kőnig’s Lemma in ZF. However, we prove that there is a model of ZF where the above statement fails.
Keywords: Axiom of Choice, Kőnig's Lemma, Brooks’ theorem, distinguishing proper coloring, total coloring, list-distinguishing proper coloring
Published in RUP: 22.10.2025; Views: 280; Downloads: 1
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4. k-Domination ivariants on Kneser graphsBoštjan Brešar, Tanja Dravec, María Gracia Cornet, Michael A. Henning, 2025, original scientific article Abstract: In this follow-up to work of M.G. Cornet and P. Torres from 2023, where the k-tuple domination number and the 2-packing number in Kneser graphs K(n, r) were studied, we are concerned with two variations, the k-domination number, γ_k(K(n, r)), and the k-tuple total domination number,
γ_{t × k}(K(n, r)), of K(n, r). For both invariants we prove monotonicity results by showing that γ_k(K(n, r)) ≥ γ_k(K(n + 1, r)) holds for any n ≥ 2(k + r), and γ_{t × k}(K(n, r)) ≥
γ_{t × k}(K(n + 1, r)) holds for any n ≥ 2r + 1. We prove that γ_k(K(n, r)) = γ_{t × k}(K(n, r)) = k + r when n ≥ r(k + r), and that in this case every γ_(k)-set and γ_(t × k)-set is a clique, while γ_k(r(k + r) − 1, r) = γ_{t × k}(r(k + r) − 1, r) = k + r + 1, for any k ≥ 2. Concerning the 2-packing number, ρ₂(K(n, r)), of K(n, r), we prove the exact values of ρ₂(K(3r − 3, r)) when r ≥ 10, and give sufficient conditions for ρ₂(K(n, r)) to be equal to some small values by imposing bounds on r with respect to n. We also prove a version of monotonicity for the 2-packing number of Kneser graphs.
Keywords: Kneser graphs, k-domination, k-tuple total domination, 2-packing
Published in RUP: 22.10.2025; Views: 259; Downloads: 1
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5. Mutual-visibility problems in Kneser and Johnson graphsGülnaz Boruzanlı Ekinci, Csilla Bujtás, 2025, original scientific article Abstract: Let G be a connected graph and X ⊆ V(G). By definition, two vertices u and v are X-visible in G if there exists a shortest u, v-path with all internal vertices being outside of the set X. The largest size of X such that any two vertices of G (resp. any two vertices from X) are X-visible is the total mutual-visibility number (resp. the mutual-visibility number) of G.
In this paper, we determine the total mutual-visibility number of Kneser graphs, bipartite Kneser graphs, and Johnson graphs. The formulas proved for Kneser, and bipartite Kneser graphs are related to the size of transversal-critical uniform hypergraphs, while the total mutual-visibility number of Johnson graphs is equal to a hypergraph Turán number. Exact values or estimations for the mutual-visibility number over these graph classes are also established.
Keywords: mutual-visibility set, total mutual-visibility set, Kneser graph, bipartite Kneser graph, Johnson graph, Turán-type problem, covering design
Published in RUP: 22.10.2025; Views: 295; Downloads: 6
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6. Adjacent vertex distinguishing total coloring of corona product of graphsHanna Furmańczyk, Rita Zuazua, 2025, original scientific article Abstract: An adjacent vertex distinguishing total k-coloring f of a graph G is a proper total k-coloring of G such that no pair of adjacent vertices has the same color sets, where the color set at a vertex v, C_f^G(v), is {f(v)} ∪ {f(vu)|u ∈ V(G), vu ∈ E(G)}. In 2005 Zhang et al. posted the conjecture (AVDTCC) that every simple graph G has adjacent vertex distinguishing total (Δ(G) + 3)-coloring. In this paper we confirm the conjecture for many types of coronas, in particular for generalized, simple and l-coronas of graphs, not relating the results to particular graph classes of the factors.
Keywords: corona graph, l-corona, generalized corona graph, adjacent vertex distinguishing total coloring, AVDTC Conjecture
Published in RUP: 21.10.2025; Views: 286; Downloads: 1
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7. Indicated total domination gameMichael A. Henning, Douglas F. Rall, 2025, original scientific article Abstract: A vertex u in a graph G totally dominates a vertex v if u is adjacent to v in G. A total dominating set of G is a set S of vertices of G such that every vertex of G is totally dominated by a vertex in S. The indicated total domination game is played on a graph G by two players, Dominator and Staller, who take turns making a move. In each of his moves, Dominator indicates a vertex v of the graph that has not been totally dominated in the previous moves, and Staller chooses (or selects) any vertex adjacent to v that has not yet been played, and adds it to a set D that is being built during the game. The game ends when every vertex is totally dominated, that is, when D is a total dominating set of G. The goal of Dominator is to minimize the size of D, while Staller wants just the opposite. Providing that both players are playing optimally with respect to their goals, the size of the resulting set D is the indicated total domination number of G, denoted by γti(G). In this paper we present several results on indicated total domination game. Among other results we prove that the indicated total domination number of a graph is bounded below by the well studied upper total domination number.
Keywords: total domination game, indicated total domination game
Published in RUP: 21.10.2025; Views: 283; Downloads: 1
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8. Lažni prijatelji med samostalniki s končnicami -ant in -ent : diplomsko deloAmila Paunović, 2022, undergraduate thesis Keywords: false friends, nouns, suffixes -ant/-ent, dictionary, total false friends, partial false friends, morphological false friends, orthographical false friends, Slovene language, English language
Published in RUP: 13.10.2022; Views: 4020; Downloads: 71
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9. Total positivity of Toeplitz matrices of recursive hypersequencesTomislav Došlić, Ivica Martinjak, Riste Škrekovski, 2019, original scientific article Keywords: total positivity, totally positive matrix, Toeplitz matrix, Hankel matrix, hyperfibonacci sequence, log-concavity
Published in RUP: 03.01.2022; Views: 2001; Downloads: 32
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10. Mathematical aspects of Wiener indexMartin Knor, Riste Škrekovski, Aleksandra Tepeh, 2016, original scientific article Abstract: The Wiener index (i.e., the total distance or the transmission number), defined as the sum of distances between all unordered pairs of vertices in a graph, is one of the most popular molecular descriptors. In this article we summarize some results, conjectures and problems on this molecular descriptor, with emphasis on works we were involved in.
Keywords: Wiener index, total distance, topological index, molecular descriptor, chemical graph theory
Published in RUP: 03.01.2022; Views: 3834; Downloads: 49
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