71. Posplošitev Lijeve domneve in popolna klasifikacija cikličnih m-(D)CI-grup : magistrsko deloLuka Šinkovec, 2023, master's thesis Keywords: (un)directed Cayley graph, cyclic group, (un)directed circulant graph, Cayley isomorphism, (un)directed CI-graph, (D)CI-group, m-(D)CI-group, key, generalised multiplier
Published in RUP: 11.09.2023; Views: 2053; Downloads: 30
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77. Divergence zero quaternionic vector fields and Hamming graphsJasna Prezelj, Fabio Vlacci, 2020, original scientific article Abstract: We give a possible extension of the definition of quaternionic power series, partial derivatives and vector fields in the case of two (and then several) non commutative (quaternionic) variables. In this setting we also investigate the problem of describing zero functions which are not null functions in the formal sense. A connection between an analytic condition and a graph theoretic property of a subgraph of a Hamming graph is shown, namely the condition that polynomial vector field has formal divergence zero is equivalent to connectedness of subgraphs of Hamming graphs ▫$H(d, 2)$▫. We prove that monomials in variables ▫$z$▫ and ▫$w$▫ are always linearly independent as functions only in bidegrees ▫$(p, 0)$▫, ▫$(p, 1)$▫, ▫$(0, q)$▫, ▫$(1, q)$▫ and ▫$(2, 2)$▫.
Keywords: quaternionic power series, bidegree full functions, Hamming graph, linearly independent quaternionic monomials
Published in RUP: 03.01.2022; Views: 2639; Downloads: 21
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79. Splittable and unsplittable graphs and configurationsNino Bašić, Jan Grošelj, Branko Grünbaum, Tomaž Pisanski, 2019, original scientific article Abstract: We prove that there exist infinitely many splittable and also infinitely many unsplittable cyclic ▫$(n_3)$▫ configurations. We also present a complete study of trivalent cyclic Haar graphs on at most 60 vertices with respect to splittability. Finally, we show that all cyclic flag-transitive configurations with the exception of the Fano plane and the Möbius-Kantor configuration are splittable.
Keywords: configuration of points and lines, unsplittable configuration, unsplittable graph, independent set, Levi graph, Grünbaum graph, splitting type, cyclic Haar graph
Published in RUP: 03.01.2022; Views: 2317; Downloads: 22
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80. A note on acyclic number of planar graphsMirko Petruševski, Riste Škrekovski, 2017, original scientific article Abstract: The acyclic number ▫$a(G)$▫ of a graph ▫$G$▫ is the maximum order of an induced forest in ▫$G$▫. The purpose of this short paper is to propose a conjecture that ▫$a(G)\geq \left( 1-\frac{3}{2g}\right)n$▫ holds for every planar graph ▫$G$▫ of girth ▫$g$▫ and order ▫$n$▫, which captures three known conjectures on the topic. In support of this conjecture, we prove a weaker result that ▫$a(G)\geq \left( 1-\frac{3}{g} \right)n$▫ holds. In addition, we give a construction showing that the constant ▫$\frac{3}{2}$▫ from the conjecture cannot be decreased.
Keywords: induced forest, acyclic number, planar graph, girth
Published in RUP: 03.01.2022; Views: 2164; Downloads: 22
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