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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.

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The aim of the article was to find out the optimal capital structure of the companies in relation to their maximum performance. To reach this aim, the data of the companies operating in the field of heat industry of the Slovak Republic were used. As the first method, a correlation matrix was applied. It was found out that there is statistically significant relationship between capital structure indicators and performance of the companies. Due to the lack of data in time series, the authors were not able to apply multiple regression model to assess the impact of these indicators on performance. Therefore, a method of modelling was used to analyze the impact of the change in capital structure on performance. Modelling was based on the principle of a gradual change in the capital structure in favor of debt. By the increase in debt, it was confirmed that there was a change in the values of selected indicators. In the course of analysis, it was confirmed that the value of EVA equity increased with the rising indebtedness by which the proposition I of the modified MM theory was supported. The performance expressed by EVA entity indicator is at its minimum when the capital structure is 90:10 in favor of equity. By increasing the debt, EVA entity rises. Based on these results, it can be stated that the performance of selected companies increases when the share of debt also rises, even when taking into account the rising financial risks.