Introduction

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Abstract We present those definitions and theorems in graph theory that are assumed throughout this book. Further explanation of these terms, together with the proofs of stated results, can be found in the standard texts listed below, although not all of the terminology is standardized. Definitions and results not included here are introduced later, as needed. A graph G consists of a finite non-empty set V (G) of elements called vertices and a finite set E(G) of distinct unordered pairs of distinct elements of V(G) called edges (see Fig. 1.1). We call V(G) the vertex set of G and E(G) the edge set of G; these are sometimes abbreviated to V and E, respectively. The number n of vertices of G is the order of G, and the number of edges of G is denoted by m. The edge {v, w} (where v and w are vertices of G) is often denoted by v w.