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“Elaboration of the Mathematical and Algorithmic Methods of Information Processing based on the Structural Analysis of Geodetic Graphs”. Thesis of application to receive the doctoral degree in Engineering Sciences, in the speciality 05.13.04 Automated Systems of Control and Information Processing, Odessa State Polytechnic University, Odessa, UKRAINE, 1997. The goals of this dissertational work were to research the structural description of geodetic graphs in terms of their minimal even circuits, to establish a new approach to the problem of constructing new classes of geodetic and bigeodetic graphs, to carry out the structural analysis of information transmission complex systems based on Geodetic Graph Theory. For the first time, the enumeration problem of geodetic graphs was proposed. The enumeration methods of geodetic graphs which are homeomorphic to a given geodetic one were elaborated. Using elements of Combinatorial Theory, the general number of geodetic graphs homeomorphic to a complete graph and the Petersen graph has been calculated. K-Geodetic Graph Theory has been used to construct, from the topological point of view, computer networks of higher security and speed of information transmission with limitations in cost.
Publications: 1. Vostrov G., Frasser C. Block-Designs, Geodetic Graphs and Cluster-analysis, Combinatorial-Statistical Methods of Analysis and Information Processing, Odessa, 1990, p.84 (In Russian). 2. Frasser C. Optimal Structures of Information Systems in the Sphere of Analysis and Social-Economic Information Processing, Conference of Young Scientists, Odessa, 1994, pp. 44-45 (In Russian). 3. Vostrov G., Frasser C. Geodetic Graphs and Information Networks, International Conference: Economic Problems of the Development of Industrial Production, Odessa, 1995, pp.152-153 (In Russian). 4. Vostrov G., Frasser C. On the Construction and Enumeration of some Classes of Geodetic Graphs, Publications of the Scientific-Technical Library of Ukraine, No. 1663, 1995, 40 p. (In Russian). 5.Vostrov G., Frasser C. Characterization of Geodetic Graphs, Publications of the Scientific-Technical Library of Ukraine, No. 1664, 1995, 17 p. (In Russian). 6. Frasser C. K-geodetic Graphs and their Application to the Topological Design of Computer Networks, Argentinean Workshop of Theoretical Computer Science, SADIO, 1999, pp. 187-203 (In Spanish). 7. Frasser C. On the Teaching of Basic Sciences in Engineering using Mathematical Modelling, I National Seminar of the Development of Thought in Higher Education, Bogota, Colombia, August, 2001 (In Spanish). 8. Frasser C. On the Possibility of a Connection between the Construction of a Class of Bigeodetic Blocks and the Existence Problem for Biplanes, 2007. 9. Frasser C. Graph Theory and the Problem of Coloring Octahedrons with Six Colors as a Generalization of the Four-Colored Cube Game, 2010. 10. Frasser C. A Relationship that expresses an Electron’s Relativistic Mass in Terms of its Relativistic Wavelength, 2010.
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