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: 975; Downloads: 21
 Full text (310,27 KB) |
2. 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
Full text (261,26 KB) |
3. 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: 1112; Downloads: 33
Full text (434,58 KB) |
