1291. Roman domination of cartesian bundles of cycles over cyclesSimon Brezovnik, Janez Žerovnik, 2025, original scientific article Abstract: A Roman dominating function $f$ of a graph $G(V, E)$ assigns labels from the set $\{0,1,2\}$ to vertices such that every vertex labeled $0$ has a neighbor labeled $2$. The weight of an RDF $f$ is defined as $w(f) = \sum_{v \in V} f(v)$, and the Roman domination number, $\gamma_R(G)$, is the minimum weight among all RDFs of $G$. This paper studies the domination and Roman domination numbers in Cartesian bundles of cycles. Furthermore, the constructed optimal patterns improve known bounds and suggest even better bounds might be achieved by combining patterns, especially for bundles involving shifts of order $4k$ and $5k$.
Keywords: Roman domination, domination, graph bundles, Roman graphs
Published in DiRROS: 21.08.2025; Views: 276; Downloads: 152
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1292. Edge-transitive cubic graphs: analysis, cataloguing and enumerationMarston D. E. Conder, Primož Potočnik, 2026, original scientific article Abstract: This paper deals with finite cubic (3-regular) graphs whose automorphism group acts transitively on the edges of the graph. Such graphs split into two broad classes, namely arc-transitive and semisymmetric cubic graphs, and then these divide respectively into 7 types (according to a classification by Djoković and Miller (1980) [17]) and 15 types (according to a classification by Goldschmidt (1980) [23]), in terms of certain group amalgams. Such graphs of small order were previously known up to orders 2048 and 768, respectively, and we have extended each of the two lists of all such graphs up to order 10000. Before describing how we did that, we carry out an analysis of the 22 amalgams, to show which of the finitely-presented groups associated with the 15 Goldschmidt amalgams can be faithfully embedded in one or more of the other 21 (as subgroups of finite index), complementing what is already known about such embeddings of the 7 Djoković-Miller groups in each other. We also give an example of a graph of each of the 22 types, and in most cases, describe the smallest such graph, and we then use regular coverings to prove that there are infinitely many examples of each type. Finally, we discuss the asymptotic enumeration of the graph orders, proving that if $f_{\mathcal C}(n)$ is the number of cubic edge-transitive graphs of type ${\mathcal C}$ on at most $n$ vertices, then there exist positive real constants $a$ and $b$ and a positive integer $n_0$ such that $n^{a \log(n)} \le f_{\mathcal C}(n) \le n^{b \log(n)}$ for all $n\ge 0$.
Keywords: groups, graphs, symmetry, amalgams, cover
Published in DiRROS: 21.08.2025; Views: 260; Downloads: 133
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1293. Multiphase structure after heat treatment enables a superior strength-plasticity combination in Y-modified ADC12 aluminum alloysWeiye Chen, Linhao Liu, Lai Wei, Nan Jia, Guihong Geng, 2025, original scientific article Keywords: ADC12 aluminum alloy, Y-modification, T6 heat treatment, deep etching, mechanical properties, orthogonal analysis
Published in DiRROS: 20.08.2025; Views: 433; Downloads: 193
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1294. Research on reflection cracking characteristics of warm-mix recycled asphalt mortar under the effect of freeze-thaw cyclesJian Gao, Zhiqiang Liu, Chao Li, Lan Wang, Yudong Ma, 2025, original scientific article Keywords: warm-mix recycled asphalt mortar, freeze-thaw cycle, reflection cracking characteristics, digital image correlation technology, cracking damage factor
Published in DiRROS: 20.08.2025; Views: 406; Downloads: 193
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1295. Effect of catalyst support on dihydroeugenol hydrodeoxygenation on low cost FeNi catalyst to produce renewable alkane fuelZuzana Vajglová, Päivi Mäki-Arvela, Olha Yevdokimova, Mark Martinez-Klimov, Irina Simakova, Kari Eränen, Teija Tirri, Jessi E. S. van Hoeven, Anssi Peuronen, Matej Huš, Blaž Likozar, 2025, original scientific article Published in DiRROS: 20.08.2025; Views: 304; Downloads: 162
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1297. Merging heterogeneous graphitic carbon nitride photocatalysis with cobaloxime catalysis in uphill dehydrogenative synthesis of anilinesSonia Zoltowska, Stefano Mazzanti, Sara Stolfi, Jingsan Xu, Matej Huš, Ana Oberlintner, Matic Pavlin, Paolo Ghigna, Blaž Likozar, Piero Torelli, 2025, original scientific article Published in DiRROS: 20.08.2025; Views: 364; Downloads: 193
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