Preliminaries

**1. Graph theory**

This section presents the basic definitions, terminology and notation of graph theory, along with some fundamental results. Further information can be found in the many standard books on the subject – for example, Bondy and Murty [1], Chartrand, Lesniak and Zhang [2], Gross and Yellen [3] or West [5], or, for a simpler treatment, Marcus [4] or Wilson [6].

**Graphs**

A *graph G* is a pair of sets (*V*, *E*), where *V* is a finite non-empty set of elements called *vertices*, and *E* is a finite set of elements called *edges*, each of which has two associated vertices. The sets *V* and *E* are the *vertex-set* and *edge-set* of *G*, and are ...

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