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On a conjecture about the ratio of Wiener index in iterated line graphs
Katarína Hriňáková, Martin Knor, Riste Škrekovski, 2018, izvirni znanstveni članek

Ključne besede: Wiener index, line graph, tree, iterated line graph
Objavljeno v RUP: 03.01.2022; Ogledov: 1261; Prenosov: 33
.pdf Celotno besedilo (391,35 KB)

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: 1003; Prenosov: 16
.pdf Celotno besedilo (354,73 KB)

Classification of cubic vertex-transitive tricirculants
Primož Potočnik, Micael Toledo, 2020, izvirni znanstveni članek

Ključne besede: graph, cubic, semiregular automorphism, tricirculant, vertex-transitive
Objavljeno v RUP: 03.01.2022; Ogledov: 953; Prenosov: 40
.pdf Celotno besedilo (1,18 MB)

Regular polygonal systems
Jurij Kovič, 2019, izvirni znanstveni članek

Ključne besede: regular polygonal system, boundary code, face vector, symmetry group, reconstructibility from the boundary
Objavljeno v RUP: 03.01.2022; Ogledov: 946; Prenosov: 17
.pdf Celotno besedilo (353,82 KB)

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: 1010; Prenosov: 19
.pdf Celotno besedilo (355,79 KB)

Semiregular automorphisms in vertex-transitive graphs with a solvable group of automorphisms
Dragan Marušič, 2017, izvirni znanstveni članek

Opis: It has been conjectured that automorphism groups of vertex-transitive (di)graphs, and more generally 2-closures of transitive permutation groups, must necessarily possess a fixed-point-free element of prime order, and thus a non-identity element with all orbits of the same length, in other words, a semiregular element. The known affirmative answers for graphs with primitive and quasiprimitive groups of automorphisms suggest that solvable groups need to be considered if one is to hope for a complete solution of this conjecture. It is the purpose of this paper to present an overview of known results and suggest possible further lines of research towards a complete solution of the problem.
Ključne besede: solvable group, semiregular automorphism, fixed-point-free automorphism, polycirculant conjecture
Objavljeno v RUP: 03.01.2022; Ogledov: 970; Prenosov: 17
.pdf Celotno besedilo (235,26 KB)

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