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1.
Divergence zero quaternionic vector fields and Hamming graphs
Jasna Prezelj, Fabio Vlacci, 2020, izvirni znanstveni članek

Opis: 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 ▫$(2, 2)$▫.
Ključne besede: quaternionic power series, bidegree full functions, Hamming graph, linearly independent quaternionic monomials
Objavljeno v RUP: 03.01.2022; Ogledov: 903; Prenosov: 16
.pdf Celotno besedilo (354,73 KB)

2.
Splittable and unsplittable graphs and configurations
Nino Bašić, Jan Grošelj, Branko Grünbaum, Tomaž Pisanski, 2019, izvirni znanstveni članek

Opis: 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.
Ključne besede: configuration of points and lines, unsplittable configuration, unsplittable graph, independent set, Levi graph, Grünbaum graph, splitting type, cyclic Haar graph
Objavljeno v RUP: 03.01.2022; Ogledov: 914; Prenosov: 19
.pdf Celotno besedilo (355,79 KB)

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