Geometric representations and symmetries of graphs, maps and other discrete structures and applications in science

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Geometric and other representations of graphs and graph based combinatorial structures have important applications in mathematics, computer science, social networks, chemistry, bioinformatics, etc. The main goal of the project is to develop a coherent theory of graph representations with emphasis on symmetric and near symmetric structures or products. The research will be followed by applications of the acquired knowledge to geometrically rich combinatorial structures like configurations, maps and polytopes, as well as to usually less symmetric large networks. The motivation for research will arise mainly from applications in mathematical chemistry, bioinformatics and social networks.The project consists of 5 themes. In each theme, the research is carried out while deliverables include scientific publications, dissemination, establishing of censuses and the implementation of relevant computer code in Magma, GAP, Pajek and Sage. The dissemination of results will include seminars, workshops, education of students and organization of one major international conference.Theme1: Representations and structure of graphs and other discrete structures: Development of coherent representation theory by integrating the results of research.Theme2: Near symmetric structures or products. Representations related to graph products using (algebraic) structures that give rise to highly regular and/or symmetric families of graphs.Theme3: Representations of symmetric graphs. Use of symmetries of highly symmetric graph for obtaining graph representations.Theme4: Representations of configurations, maps and polytopes. Structural properties of configurations, maps and polytopes are studied through symmetries with a goal of finding relevant geometrical representations for combinatorial structures.Theme5: Representations of large networks and applications in chemistry, bioinformatics and social networks: Applications of representation theory and algorithms in other disciplines especially in large networks.