Ioana Dumitriu

Fundamentals of Graph Theory

Graphs are simple objects with relatively complex properties, that help frame a tremendous number of problems in engineering, computer science, physics, mathematics, etc. We will examine some of the fundamental properties of graphs, in particular those that describe the "neighborhood" structure (and speak of how close vertices are from each other). Toward the end of the series we will introduce simple probability and speak of the random graph as a model for many structures of interest in the modern world.