ABSTRACT
Most graph theorists use personalized terminology in their books, papers, and lectures. Some authors actually define a "graph" as a graph, but others intend such alternatives as multigraph, pseudograph, directed graph, or network. It is customary to represent a graph by means of a diagram and to refer to it as the graph. There are several variations of graphs which deserve mention. The chapter discusses the basic structure of connected and disconnected graphs. A special class of intersection graphs was discovered in the field of genetics by S. Benzer when he suggested that a string of genes representing a bacterial chromosome be regarded as a closed interval on the real line. It is rather convenient to be able to express the structure of a given graph in terms of smaller and simpler graphs. It is also of value to have notational abbreviations for graphs which occur frequently.
