1. Clar and Fries structures for fullerenesPatrick W. Fowler, Wendy Myrvold, Rebecca L. Vandenberg, Elizabeth J. Hartung, Jack E. Graver, 2026, original scientific article Abstract: Fries and Clar numbers are qualitative indicators of stability in conjugated π systems. For a given Kekulé structure, call any hexagon that contains three double bonds benzenoid. The Fries number is the maximum number of benzenoid hexagons, whereas the Clar number is the maximum number of independent benzenoid hexagons, in each case taken over all Kekulé structures. A Kekulé structure that realises the Fries (Clar) number is a Fries (Clar) structure. For benzenoids, it is not known whether every Fries structure is also a Clar structure. For fullerenes C_n, it is known that some Clar structures in large examples correspond to no Fries structure. We show that Fries structures that are not Clar occur early: examples where some Fries structure is not Clar start at C_34, and examples where no Fries structure is Clar start at C_48. Hence, it is unsafe to use fullerene Fries structures as routes to Clar number. However, Fries structures often describe the neutral fullerene better than a Clar structure, e.g. in rationalising bond lengths in the experimental isomer of C_60. Conversely, an extension of Clar sextet theory suggests the notion of anionic Clar number for fullerene anions, where both pentagons and hexagons may support sextets.
Keywords: chemical graph theory, fullerenes, benzenoids, Clar, Fries, Kekule, perfect matching
Published in RUP: 22.12.2025; Views: 147; Downloads: 1
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2. Tight upper bounds for the p-anionic Clar number of fullerenesAaron Slobodin, Wendy Myrvold, Gary MacGillivray, Patrick W. Fowler, 2026, original scientific article Abstract: A fullerene is an all-carbon molecule with a polyhedral structure where each atom is bonded to three other atoms and each face is either a pentagon or a hexagon. Fullerenes correspond to 3-regular planar graphs whose faces have sizes 5 or 6. The p-anionic Clar number C_(p)(G) of a fullerene G is equal to p + h, where h is maximized over all choices of p + h independent faces (exactly p pentagons and h hexagons) the deletion of whose vertices leave a graph with a perfect matching. This definition is motivated by the chemical observation that pentagonal rings can accommodate an extra electron, so that the pentagons of a
fullerene with charge −p, compete with the hexagons to host ‘Clar sextets’ of six electrons, and pentagons will preferentially acquire the p excess electrons of the anion.
Tight upper bounds are established for the p-anionic Clar number of fullerenes for p > 0. The upper bounds are derived via graph theoretic arguments and new results on minimal cyclic-k-edge cutsets in IPR fullerenes (fullerenes that have all pentagons pairwise disjoint). These bounds are shown to be tight by infinite families of fullerenes that achieve them.
Keywords: chemical graph theory, anionic Clar number, fullerenes
Published in RUP: 21.12.2025; Views: 188; Downloads: 1
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3. Unveiling Organizational AI Adoption Patterns in Italian Companies through the Lens of the Diffusion of Innovations TheoryGrazia Garlatti Costa, Francesco Venier, Roberto Pugliese, 2025, original scientific article Abstract: This paper investigates the adoption and integration of artificial intelligence (AI) technologies within a sample of 237 Italian enterprises using the Diffusion of Innovations (DOI) theory as the theoretical framework. It examines the characteristics of companies leading in AI adoption, evaluating their alignment with the innovator and early adopter profiles defined by Everett Rogers in 2003 within the DOI framework. The research emphasizes AI’s significant role in enhancing operational efficiency, fostering innovation, securing competitive advantage, and driving long-term growth. It also identifies challenges such as lack of skills, data management issues, and ethical concerns. Our findings contribute empirical evidence to the academic literature on the DOI theory, addressing the underexplored context of AI in Italy. The study provides a nuanced perspective on AI’s impact on employment and sets a foundation for future research, offering managerial insights for strategically deploying AI.
Keywords: artificial intelligence, diffusion of innovations theory, early adopters, implementation challenges, Italian companies
Published in RUP: 18.12.2025; Views: 147; Downloads: 0
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4. Optimal bounds for zero-sum cycles. I. Odd orderRutger Campbell, J. Pascal Gollin, Kevin Hendrey, Raphael Steiner, 2025, original scientific article Abstract: 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.
Keywords: Zero-sum Ramsey theory, directed cycles, Zero-sum cycles
Published in RUP: 24.11.2025; Views: 290; Downloads: 4
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5. Exploring social interactions on the Adriatic networkŽiga Velkavrh, 2025, original scientific article Abstract: 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.
Keywords: Adriatic, anti-coordination games, coordination games, game theory, Nash equilibrium, networks, prisoner’s dilemma, spatial games
Published in RUP: 20.11.2025; Views: 306; Downloads: 13
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6. On edge-girth-regular graphs: lower bounds and new familiesIstván Porupsánszki, 2025, original scientific article Abstract: An edge-girth-regular graph egr(n, k, g, λ) is a k-regular graph of order n, girth g and with the property that each of its edges is contained in exactly λ distinct g-cycles. We present new families of edge-girth regular graphs arising from generalized quadrangles and pencils of elliptic quadrics.
An egr(n, k, g, λ) is called extremal for the triple (k, g, λ) if n is the smallest order of any egr(n, k, g, λ). We give new lower bounds for the order of extremal edge-girth-regular graphs using properties of the eigenvalues of the adjacency matrix of a graph.
Keywords: cage problem, extremal graph theory, generalized polygons, ovoids
Published in RUP: 22.10.2025; Views: 328; Downloads: 1
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7. Ehrhart limitsBenjamin Braun, McCabe Olsen, 2025, original scientific article Abstract: We introduce the definition of an Ehrhart limit, that is, a formal power series with integer coefficients that is the limit in the ring of formal power series of a sequence of Ehrhart h*-polynomials. We identify a variety of examples of sequences of polytopes that yield Ehrhart limits, with a focus on reflexive polytopes and simplices.
Keywords: Ehrhart theory, lattice simplices, reflexive polytopes
Published in RUP: 16.09.2025; Views: 361; Downloads: 8
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9. Selected topics on Wiener indexMartin Knor, Riste Škrekovski, Aleksandra Tepeh, 2024, original scientific article Keywords: graph distance, Wiener index, average distance, topological index, molecular descriptor, chemical graph theory
Published in RUP: 26.05.2025; Views: 757; Downloads: 7
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