Abstract
One area in which a great deal of work has been done in the development of parallel algorithms is that of graph algorithms. An undirected graph G is a pair of (V, E), where V is a finite set of points called vertices and E is a finite set of arcs called edges. An edge e∈E is an unordered pair (v,u) where v,u∈V and vertices v and u are connected. Similarly, a directed graph G is a pair of (V,E) where V is a finite set of points called vertices and e = (v,u)∈ E is an ordered pair of vertices, meaning that there is a connection from v to u. Throughout this chapter the term graph refer to both directed and undirected graphs. Figure 6.1 illustrates a directed and an undirected graph. Many definitions are common to directed and undirected graphs, and in the following some of these definitions are presented. In addition, there are many introductory texts, for example [Sahni 85], which may be consulted.
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