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## Introduction

LOWELL W. BEINEKE and ROBIN J. WILSON

1. Graph theory

2. Graphs in the plane

3. Surfaces

4. Graphs on surfaces

References

### 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, Chartrand and Lesniak [1] , Gross and Yellen [2], West [3] or (for a simpler treatment) Wilson [4].

#### 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 (which may be the same). The sets V and E are the vertex-set and edge-set of G, and are sometimes ...

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