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A numerical quantity which characterize the whole structure of a graph is called a topological index. The concept of Randić (Rα), atom-bond connectivity (ABC) and geometric-arithmetic (GA) topological indices were established in chemical graph theory based on vertex degrees. In this paper, we study carbon nanotube network which is motivated by molecular structure of regular hexagonal lattice, and determine Rα, ABC and GA indices for this important class of networks.

In this paper, the following research problem was addressed: Is DEA (Data Envelopment Analysis) method a suitable alternative to Altman model in predicting the risk of bankruptcy? Based on the above-mentioned research problem, we formulated the aim of the paper: To apply DEA method for predicting the risk of bankruptcy and to compare its results with the results of Altman model. The research problem and the aim of the paper follow the research of authors aimed at the application of methods which are appropriate for measuring business financial health, performance and competitiveness as well as for predicting the risk of bankruptcy. To address the problem, the following methods were applied: financial ratios, Altman model for private non-manufacturing firms and DEA method. When applying DEA method, we formulated input-oriented DEA CCR model. We found that DEA method is an appropriate alternative to Altman model in predicting the risk of possible business bankruptcy. The important conclusion is that DEA allows us to apply not only outputs but also inputs. Since prediction models do not include these indicators, DEA method appears to be the right choice. We recommend, especially for Slovak companies, to apply cost ratio when calculating risk of bankruptcy.

The current trend at universities is to offer to students the study programs with the subjects taught in English. We are interested in the facts what competences and associated learning outcomes can be achieved by the students. Therefore, the main objective of this paper is the pedagogical and statistical analysis of the study outcomes. We have decided to compare the examination results of the selected subjects and determine whether study outcomes of the subjects are statistically dependent. We have obtained the data for the analysis from the compulsory subjects of Mathematics (taught in English and in the Slovak language) and from the subject English for Specific Purposes I. We have analysed the results of the study groups from the Faculty of European Studies and Regional Development at the Slovak University of Agriculture in Nitra.

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