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

几何和其他表示的图形和图形为基础的组合结构在数学，计算机科学，社交网络，化学，生物信息学等的项目的主要目标是开发一个连贯的理论，强调对称和近对称结构或产品的图形表示。研究之后将应用所获得的知识，几何丰富的组合结构，如配置，地图和多面体，以及通常不对称的大型网络。研究的动机主要来自于数学化学、生物信息学和社交网络的应用。在每一个主题中，都进行了研究，而交付成果包括科学出版物、传播、建立普查和在Magma、GAP、Pajek和Sage中执行相关计算机代码。成果的传播将包括研讨会、讲习班、学生教育和组织一次重大国际会议。主题1：图和其他离散结构的表示和结构：通过整合研究结果发展连贯表示理论。使用（代数）结构的图积的表示，这些结构产生高度正则和/或对称的图族。主题3：对称图的表示。利用高度对称图的对称性获得图的表示。主题4：构形、映射和多面体的表示。通过对称性来研究构型、映射和多面体的结构性质，目的是找到组合结构的相关几何表示。主题5：大型网络的表示及其在化学、生物信息学和社交网络中的应用：表示理论和算法在其他学科特别是大型网络中的应用。

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.