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Some remarks on Balaban and sum-Balaban index
Martin Knor, Jozef Komorník, Riste Škrekovski, Aleksandra Tepeh, 2020, izvirni znanstveni članek

Opis: In the paper we study maximal values of Balaban and sum-Balaban index, and correct some results appearing in the literature which are only partially correct. Henceforth, we were able to solve a conjecture of M. Aouchiche, G. Caporossi and P. Hansen regarding the comparison of Balaban and Randić index. In addition, we showed that for every k and large enough n, the first k graphs of order n with the largest value of Balaban index are trees. We conclude the paper with a result about the accumulation points of sum-Balaban index.
Ključne besede: topological index, Balaban index, sum-Balaban index, Randić index
Objavljeno: 03.01.2022; Ogledov: 143; Prenosov: 8
Gradivo ima več datotek! Več...

Regular antilattices
Tomaž Pisanski, Jonathan Leech, Michael Kinyon, Karin Cvetko-Vah, 2019, izvirni znanstveni članek

Opis: Antilattices ▫$(S; \vee, \wedge)$▫ for which the Green's equivalences ▫$\mathcal{L}_{(\vee)}$▫, ▫$\mathcal{R}_{(\vee)}$▫, ▫$\mathcal{L}_{(\wedge)}$▫ and ▫$\mathcal{R}_{(\wedge)}$▫ are all congruences of the entire antilattice are studied and enumerated.
Ključne besede: noncommutative lattice, antilattice, Green's equivalences, lattice of subvarieties, enumeration, partition, composition
Objavljeno: 03.01.2022; Ogledov: 125; Prenosov: 6
Gradivo ima več datotek! Več...

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: 03.01.2022; Ogledov: 118; Prenosov: 9
Gradivo ima več datotek! Več...

Divergence zero quaternionic vector fields and Hamming graphs
Jasna Prezelj-Perman, 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: 03.01.2022; Ogledov: 140; Prenosov: 7
.pdf Polno 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: 03.01.2022; Ogledov: 119; Prenosov: 6
.pdf Polno 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: 03.01.2022; Ogledov: 99; Prenosov: 6
.pdf Polno 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: 03.01.2022; Ogledov: 102; Prenosov: 7
.pdf Polno besedilo (355,79 KB)

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