An Introduction to Graph Theory
In this book you are invited to the world of the application of the graph theory to chemistry, especially on the problem how the topology of a molecule determines its reactivity toward a specific reaction and how the graphs helps you understand these relationships.
Abstract
This is a graduate-level introduction to graph theory, corresponding to a quarter-long course. It covers simple graphs, multigraphs as well as their directed analogues, and more restrictive classes such as tournaments, trees and arborescences. Among the features discussed are Eulerian circuits, Hamiltonian cycles, spanning trees, the matrix-tree and BEST theorems, proper colorings, Turan's theorem, bipartite matching and the Menger and Gallai--Milgram theorems. The basics of network flows are introduced in order to prove Hall's marriage theorem. Around a hundred exercises are included (without solutions).