Handbook of Graph Theory, 2nd Edition

Chapter 13

Natural Science & Processes

Section 13.1 Chemical Graph Theory

Ernesto Estrada

University of Strathclyde, Scotland

Danail Bonchev

Virginia Commonwealth University

Introduction

Chemical graph theory (CGT) is a branch of mathematical chemistry which deals with the nontrivial applications of graph theory to solve molecular problems. In general, a graph is used to represent a molecule by considering the atoms as the vertices of the graph and the molecular bonds as the edges. Then, the main goal of CGT is to use algebraic invariants to reduce the topological structure of a molecule to a single number which characterizes either the energy of the molecule as a whole or its orbitals, its molecular branching, structural fragments, and its ...