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 in RUP: 03.01.2022; Views: 974; Downloads: 21
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3. 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 in RUP: 03.01.2022; Views: 807; Downloads: 25
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4. A note on acyclic number of planar graphsMirko Petruševski, Riste Škrekovski, 2017, original scientific article Abstract: The acyclic number ▫$a(G)$▫ of a graph ▫$G$▫ is the maximum order of an induced forest in ▫$G$▫. The purpose of this short paper is to propose a conjecture that ▫$a(G)\geq \left( 1-\frac{3}{2g}\right)n$▫ holds for every planar graph ▫$G$▫ of girth ▫$g$▫ and order ▫$n$▫, which captures three known conjectures on the topic. In support of this conjecture, we prove a weaker result that ▫$a(G)\geq \left( 1-\frac{3}{g} \right)n$▫ holds. In addition, we give a construction showing that the constant ▫$\frac{3}{2}$▫ from the conjecture cannot be decreased.
Keywords: induced forest, acyclic number, planar graph, girth
Published in RUP: 03.01.2022; Views: 974; Downloads: 16
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5. Relative edge betweenness centralityDamir Vukičević, Riste Škrekovski, Aleksandra Tepeh, 2017, original scientific article Abstract: We introduce a new edge centrality measure - relative edge betweenness ▫$\gamma (uv) = b(uv)/\sqrt{c(u)c(v)}$▫, where ▫$b(uv$)▫ is the standard edge betweenness and ▫$c(u)$▫ is the adjusted vertex betweenness. In this alternative definition, the importance of an edge is normalized with respect to the importance of its end-vertices. This gives a better presentation of the ''local'' importance of an edge, i.e. its importance in the near neighborhood. We present sharp upper and lower bounds on this invariant together with the characterization of graphs attaining these bounds. In addition, we discuss the bounds for various interesting graph families, and state several open problems.
Published in RUP: 03.01.2022; Views: 727; Downloads: 15
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6. Mathematical aspects of fullerenesVesna Andova, František Kardoš, Riste Škrekovski, 2016, original scientific article Abstract: Fullerene graphs are cubic, 3-connected, planar graphs with exactly 12 pentagonal faces, while all other faces are hexagons. Fullerene graphs are mathematical models of fullerene molecules, i.e., molecules comprised only by carbon atoms different than graphites and diamonds. We give a survey on fullerene graphs from our perspective, which could be also considered as an introduction to this topic. Different types of fullerene graphs are considered, their symmetries, and construction methods. We give an overview of some graph invariants that can possibly correlate with the fullerene molecule stability, such as: the bipartite edge frustration, the independence number, the saturation number, the number of perfect matchings, etc.
Keywords: fullerene, cubic graph, planar graph, topological indices
Published in RUP: 03.01.2022; Views: 790; Downloads: 17
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7. Mathematical aspects of Wiener indexMartin Knor, Riste Škrekovski, Aleksandra Tepeh, 2016, original scientific article Abstract: The Wiener index (i.e., the total distance or the transmission number), defined as the sum of distances between all unordered pairs of vertices in a graph, is one of the most popular molecular descriptors. In this article we summarize some results, conjectures and problems on this molecular descriptor, with emphasis on works we were involved in.
Keywords: Wiener index, total distance, topological index, molecular descriptor, chemical graph theory
Published in RUP: 03.01.2022; Views: 1105; Downloads: 33
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