The authors demonstrate a coherent piece of mathematical chemistry in the form which is a relatively new branch in science. They apply graph theory to chemical graphs representing polycyclic conjugated hydrocarbons. The scope is mainly limited to coronoids. The area is interdisciplinary, penetrating into mathematics, chemistry and computer science. Enumerations of chemical graphs are executed by algebraic methods on one hand and computer programming on the other. The combined attack on the different problems from largely different viewpoints is supposed to be a feature of particular interest to many different scientists. The voluminous bibliography is a result of extensive studies.