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Some remarks on Balaban and sum-Balaban index
Martin Knor, Jozef Komorník, Riste Škrekovski, Aleksandra Tepeh, 2020, original scientific article

Abstract: 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.
Keywords: topological index, Balaban index, sum-Balaban index, Randić index
Published: 03.01.2022; Views: 198; Downloads: 13
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Regular antilattices
Tomaž Pisanski, Jonathan Leech, Michael Kinyon, Karin Cvetko-Vah, 2019, original scientific article

Abstract: 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.
Keywords: noncommutative lattice, antilattice, Green's equivalences, lattice of subvarieties, enumeration, partition, composition
Published: 03.01.2022; Views: 162; Downloads: 9
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On a conjecture about the ratio of Wiener index in iterated line graphs
Katarína Hriňáková, Martin Knor, Riste Škrekovski, 2018, original scientific article

Keywords: Wiener index, line graph, tree, iterated line graph
Published: 03.01.2022; Views: 164; Downloads: 13
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Divergence zero quaternionic vector fields and Hamming graphs
Jasna Prezelj-Perman, 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: 03.01.2022; Views: 203; Downloads: 9
.pdf Full text (354,73 KB)

Classification of cubic vertex-transitive tricirculants
Primož Potočnik, Micael Toledo, 2020, original scientific article

Keywords: graph, cubic, semiregular automorphism, tricirculant, vertex-transitive
Published: 03.01.2022; Views: 165; Downloads: 9
.pdf Full text (1,18 MB)

Regular polygonal systems
Jurij Kovič, 2019, original scientific article

Keywords: regular polygonal system, boundary code, face vector, symmetry group, reconstructibility from the boundary
Published: 03.01.2022; Views: 141; Downloads: 8
.pdf Full text (353,82 KB)

Splittable and unsplittable graphs and configurations
Nino 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: 03.01.2022; Views: 146; Downloads: 10
.pdf Full text (355,79 KB)

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