Iskanje po repozitoriju

Opis: A nut graph is a simple graph of order 2 or more for which the adjacency matrix has a single zero eigenvalue such that all nonzero kernel eigenvectors have no zero entry (i.e. are full). It is shown by construction that every finite group can be represented as the group of automorphisms of infinitely many nut graphs. It is further shown that such nut graphs exist even within the class of regular graphs; the cases where the degree is 8, 12, 16, 20 or 24 are realised explicitly.
Ključne besede: nut graph, graph automorphism, automorphism group, nullity, graph spectra, f-universal
Objavljeno v RUP: 25.11.2025; Ogledov: 463; Prenosov: 4
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Opis: For a finite (not necessarily abelian) group Γ, let n(Γ) denote the smallest positive integer $n$ such that for each labelling of the arcs of the complete digraph of order n using elements from Γ, there exists a directed cycle such that the arc-labels along the cycle multiply to the identity. Alon and Krivelevich [2] initiated the study of the parameter n(.) on cyclic groups and proved n(Z_q) = O(q log q). This was later improved to a linear bound of n(Γ) <= 8|Γ| for every finite abelian group Γ by Mészáros and the last author [8], and then further to n(Γ) <= 2|Γ|-1 for every non-trivial finite group independently by Berendsohn, Boyadzhiyska and Kozma [3] as well as by Akrami, Alon, Chaudhury, Garg, Mehlhorn and Mehta [1]. In this series of two papers we conclude this line of research by proving that n(Γ) < |Γ|+1 for every finite group Γ, which is the best possible such bound in terms of the group order and precisely determines the value for all cyclic groups as n(Z_q) = q+1. In the present paper we prove the above result for all groups of odd order. The proof for groups of even order needs to overcome substantial additional obstacles and will be presented in the second part of this series.
Ključne besede: Zero-sum Ramsey theory, directed cycles, Zero-sum cycles
Objavljeno v RUP: 24.11.2025; Ogledov: 317; Prenosov: 4
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Opis: This paper explores social interactions on the Adriatic network consisting of six countries surroundingthe Adriatic Sea. Using game theory, we analyze how three well-known classes of 2x2 strategic games, namely Prisoner’s dilemma, anti-coordination and coordination games, would be played on the Adriatic network. We determine all Nash equilibria, i.e., steady states, and obtain two main results. First, anti-coordination games on the Adriatic network always induce multiple (4, 5, 7 or 12) Nash equilibria that vary with payoffs and may differin efficiency. Second, coordination games on the Adriatic network have only trivial equilibria, unless a specific condition on payoffs is met, in which case two new equilibria emerge. Our findings may be of great interest for policy makers and other scholars interested in maritime pollution control and other water-related problems, as well as biodiversity conservation, as they indicate at which maritime borders (anti)coordination issues and resulting inefficiencies may arise. Knowing that, one may give special attention to the critical maritime borders and take extra care there, thus helping to prevent potential catastrophic events. Finally, our study can also be used for academic purposes, e.g., in classroom, to demonstrate how to perform a complete Nash equilibrium analysis on some real-world network which has a relatively simple structure.
Ključne besede: Adriatic, anti-coordination games, coordination games, game theory, Nash equilibrium, networks, prisoner’s dilemma, spatial games
Objavljeno v RUP: 20.11.2025; Ogledov: 339; Prenosov: 13
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Opis: Finger-jointed timber boards for cross-laminated timber production are typically assigned the same characteristic bending strength (fm,j,k) if produced from the same strength class, regardless of differences in their cross-sectional dimensions. To validate the relevance of this approach, this study investigated the effects of cross-sectional dimensions on the bending performance of finger-jointed timber produced from spruce (strength class: C24). A large industrial dataset of 1100 specimens, with seven thicknesses (ranging 20 to 40 mm) and variable widths, were statistically analyzed. The bending tests were performed with a constant span-to-depth ratio (l/h = 18), meaning thinner specimens had a shorter test span. Bending strength was modeled with Bayesian multilevel linear model, and the proportions of three quality-control failure modes (joint interface failure, joint base failure, and outside-joint failure) were analyzed with a zero-one-inflated Dirichlet regression. Based on the results, all groups with n ≥ 100 exceeded the declared fm,j,k of 27.6 MPa, with characteristic strengths of 43.7 MPa (+58.3 %), 40.0 MPa (+45.0 %), and 38.3 MPa (+38.8 %) for the 20-, 30-, and 40-mm thickness groups, respectively. Thinner specimens demonstrated higher bending strength with convincing evidence (pairwise contrasts PD = 100 % with 95 % HDPIs entirely below zero), while width had no credible effect (PD < 95 %). Dirichlet regression revealed shifts in failure mode proportions with varying strength. Higher bending strengths were associated with a higher proportion of joint interface failure. Outside‑joint failure was observed with a higher proportion in lower-strength and thicker specimens. Overall, assigning uniform fm,j,k to various cross-sectional dimensions proved to give adequate safety margins. Beyond the uniform fm,j,k, however, statistical evidence of a size effect on both bending strength and failure modes was observed. The magnitude of the observed size effect reflects the combined influence of increasing thickness and test span under the current quality control bending test regime, which means a coupled change in stressed volume and geometry rather than a pure cross-section scaling effect. These findings are relevant to flatwise four-point bending tests on finger-jointed boards from industrial production made with visually graded C24 spruce with thickness ranging 20 to 40 mm.
Ključne besede: wood, finger joint, strength
Objavljeno v RUP: 18.11.2025; Ogledov: 345; Prenosov: 5
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Opis: In 1965, Erdős and Pósa proved that there is an (approximate) duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality does not hold for odd cycles, and Dejter and Neumann-Lara asked in 1988 to find all pairs (l, z) of integers where such a duality holds for the family of cycles of length l modulo z. We characterise all such pairs, and we further generalise this characterisation to cycles in graphs labelled with a bounded number of abelian groups, whose values avoid a bounded number of elements of each group. This unifies almost all known types of cycles that admit such a duality, and it also provides new results. Moreover, we characterise the obstructions to such a duality in this setting, and thereby obtain an analogous characterisation for cycles in graphs embeddable on a fixed compact orientable surface.
Ključne besede: Erdős-Pósa property, cycle packing, group-labelled graph
Objavljeno v RUP: 17.11.2025; Ogledov: 391; Prenosov: 8
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