Representations of graphs and networks (coding, layouts and embeddings)

Abstract

Special representations of graphs are defined and classes of graphs which admit effective special representations are characterized. Representations of graphs by families of sets of objects of different kinds are studied, and the topological themes involved in laying out graphs on surfaces are discussed. A description is given of metric and algebraic representations of graphs in arithmetical spaces. Some results pertaining to graph representations in terms of standard operations are presented. As applications we describe results pertaining to two spheres of knowledge: automated computer design and organization of programming work on computers; and graphical representation of molecules and chemical formulas in organic and inorganic chemistry.