Graph Theory and Calculus: Ratios of Classes of Graphs

The book explores the intersection of graph theory and calculus, presenting ten distinct ratios that incorporate graph theoretical concepts. It emphasizes the significance of horizontal asymptotic behavior of these ratios as functions of graph order, particularly in large-scale applications like networks and molecular structures. By linking the average degree of a graph to the Riemann integral of these functions, it introduces the concept of area in relation to graph classes. Key topics include asymptotic convergence, chromatic numbers, and the energy of graphs, alongside explorations of sequences.