1. Some remarks on Balaban and sum-Balaban indexMartin 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: 48; Downloads: 2
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2. Regular antilatticesTomaž 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: 36; Downloads: 1
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4. Divergence zero quaternionic vector fields and Hamming graphsJasna 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: 41; Downloads: 2
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7. Total positivity of Toeplitz matrices of recursive hypersequencesTomislav Došlić, Ivica Martinjak, Riste Škrekovski, 2019, original scientific article Keywords: total positivity, totally positive matrix, Toeplitz matrix, Hankel matrix, hyperfibonacci sequence, log-concavity
Published: 03.01.2022; Views: 27; Downloads: 3
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9. 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: 03.01.2022; Views: 26; Downloads: 2
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10. Linking rings structures and semisymmetric graphsPrimož Potočnik, Steve Wilson, 2018, original scientific article Keywords: graphs, automorphism group, symmetry, locally arc-transitive graphs, symmetric graphs, cycle structure, linking ring structure
Published: 03.01.2022; Views: 46; Downloads: 1
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