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62. Optimal strategies in fractional games: vertex cover and dominationCsilla Bujtás, Günter Rote, Zsolt Tuza, 2024, original scientific article Abstract: In a hypergraph ${\cal H}=(V,{\cal E})$ with vertex set $V$ and edge set ${\cal E}$, a real-valued function $f: V \to [0, 1]$ is a fractional transversal if $\sum_{v\in E} f(v) \ge 1$ for every edge $E \in {\cal E}$. Its size is $|f| := \sum_{v \in V} f(v)$, and the fractional transversal number $\tau^\ast({\cal H})$ is the smallest possible $|f|$. We consider a game scenario where two players have opposite goals, one of them trying to minimize and the other to maximize the size of a fractional transversal constructed incrementally. We prove that both players have strategies to achieve their common optimum, and they can reach their goals using rational weights.
Keywords: fractional vertex cover, fractional transversal game, fractional domination game
Published in DiRROS: 24.01.2025; Views: 51; Downloads: 23
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63. Classification of cubic tricirculant nut graphsIvan Damnjanović, Nino Bašić, Tomaž Pisanski, Arjana Žitnik, 2024, original scientific article Abstract: A nut graph is a simple graph whose adjacency matrix has the eigenvalue zero with multiplicity one such that its corresponding eigenvector has no zero entries. It is known that there exist no cubic circulant nut graphs. A bicirculant (resp. tricirculant) graph is defined as a graph that admits a cyclic group of automorphisms having two (resp. three) orbits of vertices of equal size. We show that there exist no cubic bicirculant nut graphs and we provide a full classification of cubic tricirculant nut graphs.
Keywords: bicirculant, tricirculant, eigenvalue
Published in DiRROS: 24.01.2025; Views: 41; Downloads: 14
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64. Genomic insights into genetic diversity and seed coat color change in common bean composite populationsEva Plestenjak, Mohamed Neji, Lovro Sinkovič, Vladimir Meglič, Barbara Pipan, 2024, original scientific article Keywords: seed coat color, phenotypic variation, composite populations, whole genome sequencing
Published in DiRROS: 24.01.2025; Views: 62; Downloads: 34
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65. Zakaj in kakšno strokovno podporo potrebujejo pacienti med zdravljenjem raka : 48. strokovni seminar2024, not set Keywords: kemoterapija, biološka zdravila, alergija, imunoterapija, neželeni učinki, pacienti, psihološka podpora, parenteralna prehrana, spolnost, zborniki, elektronske knjige
Published in DiRROS: 24.01.2025; Views: 32; Downloads: 18
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66. The Sierpiński domination numberMichael A. Henning, Sandi Klavžar, Elżbieta Kleszcz, Monika Pilśniak, 2024, original scientific article Abstract: Let $G$ and $H$ be graphs and let $f \colon V(G)\rightarrow V(H)$ be a function. The Sierpiński product of $G$ and $H$ with respect to $f$, denoted by $G \otimes _f H$, is defined as the graph on the vertex set $V(G)\times V(H)$, consisting of $|V(G)|$ copies of $H$; for every edge $gg'$ of $G$ there is an edge between copies $gH$ and $g'H$ of $H$ associated with the vertices $g$ and $g'$ of $G$, respectively, of the form $(g,f(g'))(g',f(g))$. In this paper, we define the Sierpiński domination number as the minimum of $\gamma(G\otimes _f H)$ over all functions $f \colon V(G)\rightarrow V(H)$. The upper Sierpiński domination number is defined analogously as the corresponding maximum. After establishing general upper and lower bounds, we determine the upper Sierpiński domination number of the Sierpiński product of two cycles, and determine the lower Sierpiński domination number of the Sierpiński product of two cycles in half of the cases and in the other half cases restrict it to two values.
Keywords: Sierpiński graph, Sierpiński product, domination number, Sierpiński domination number
Published in DiRROS: 24.01.2025; Views: 42; Downloads: 23
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67. Rak jajčnikov : zanositev in nosečnost2024, proceedings of peer-reviewed scientific conference contributions (domestic conferences) Abstract: Predstavljamo vam zbornik znanstvenih prispevkov, ki naslavlja kompleksen odnos med rakom jajčnikov, zanositvijo in nosečnostjo. Gre za tematiko, ki v medicinskih in raziskovalnih krogih postaja vse bolj aktualna, saj tehnološki in terapevtski napredek omogočata razvoj novih pristopov, ki izboljšujejo kakovost življenja bolnic in odpirajo možnosti za ohranjanje plodnosti tudi pri onkoloških bolnicah.
Published in DiRROS: 24.01.2025; Views: 29; Downloads: 13
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