What Is Quantitative Graph Theory?

Graph theory [12,83,86] is a relatively new branch of mathematics and the main body of fundamental results dates back to the seminal contribution due toKönig [111]. Earlier contributions dealing with graphs are due to Euler [72] and Kirchhoff [104]. Importantly, Euler solved the so-called Königsberg bridge problem by introducing graph-theoretical terms that contributed to modern graph theory extensively [14,75].