The interest in the study of graph theory has increased due to its applicability in so many fields like artificial intelligence, electrical engineering, transportation system, scheduling problems, economics, chemistry and operations research.

**Definition 17.1** A **graph** *G* = (*V*, *E*) is a mathematical structure consisting of two finite sets *V* and *E*. The elements of *V* are called **vertices (or nodes)** and the elements of *E* are called edges. Each edge is associated with a set consisting of **either one** or **two vertices** called its **endpoints**.

The correspondence from edges to endpoints is called edge-endpoint function. This function is generally denoted by γ. Due to thisfunction, some authors denote graph by *G* = ...

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