ABSTRACT. The betweenness centrality of a vertex of a graph is the portion of the shortest paths between all pairs of vertices passing through a given vertex. We study upper bounds for this invariant and its relations to the diameter and average distance of a graph.
The integration of the Slovak Republic into the European Union and the globalization process create conditions that significantly reduce barriers to entry into particular markets, but, on the other hand, enhance the intensity of competition. The relevance of the study lies in the extent of the European Union’s support for the effectiveness of innovation activities in Slovakia. This paper investigates the influence of endogenous and exogenous factors on the competitiveness of Slovak enterprises over the period 2006–2018. The study is aimed at determining the causal relationship of factors that determine the competitiveness of enterprises. To investigate the relationship between the endogenous and exogenous factors, the Granger causality method is used. Mathematical models are used to identify the relationship between innovation expenditures on the one hand and different types of innovation activity with market expansion on the other. The results of the study provide a statistically significant relationship between the performance measured by the percentage of revenues of enterprises that have introduced innovations with a two-year lag and the concentration measured by the total R&D expenditure of an enterprise. The results of this study should also be used to ensure that, in the case of the Slovak SME sector, R&D expenditure is a significant driver of innovation in enterprises, as innovation in enterprises is expected to improve the quality of products and services, increase profits and expansion in domestic and foreign markets. AcknowledgmentThis paper has been supported by funds of the project VEGA No. 1/0240/20 and VEGA No. 1/0813/19 Managing the development of innovative and start-up forms of businesses in international environment and verification of INMARK concept, which has received funding from the Ministry of Education, Science, Research and Sport of the Slovak Republic.
The business environment and entrepreneurship are important elements in the economic growth of each country. The better the business environment a given country offers, the more attractive the country is for small and large companies as well as for private entrepreneurs. A high level of business competitiveness can help a country secure economic growth, especially after overcoming a crisis such as the COVID-19 pandemic. Many institutions focus on the measurement of the business environment using indices to evaluate its quality. The main goal of the present study is to evaluate the quality of the business environment through multicriteria analysis. For the period from 2018 to 2020, the data were analysed by using seven selected indices of the weighted sum approach (WSA) and the technique for order preference by similarity to ideal solution (TOPSIS) methods. The research sample included all EU countries that joined the EU at the same time in 2004. The processing of analytical data was gradually implemented by using descriptive statistics and multicriteria evaluation methods. The methods used in the multicriteria evaluation of variants determined the rankings of the individual variants in terms of the selected criteria using entropy. We concluded that the efficiency of the business environments in Cyprus, the Czech Republic, Estonia, Hungary, Poland, Latvia, Lithuania, Slovakia and Slovenia are below the EU average. Within this group of countries, Estonia, Malta and Slovenia have seen the largest regeneration of their business environment since having joined the EU.
Quality of life can be expressed as a highly subjective measure of happiness, which is an important part of many financial and non-financial decisions. The issue of quality of life, namely its quantification, is a current topic, evidenced by a number of literary sources in both foreign and domestic literature. The paper deals with this issue in the conditions of the Slovak Republic and studies the quality of life for each region of Slovakia with respect to the given indicators. In this paper, we deal with the use of the methods of multi-criteria analysis in evaluating the quality of life in Slovakia. The aim of this paper is to highlight that it is important to monitor the level of quality of life at the regional level and that one of the indicators influencing the quality of life in the region may be its location in relation to neighboring countries.
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