Abstract
A graph (undirected) can be defined as a pair (V, E) where V is a non-empty finite set and E is a family of distinct unordered pairs of distinct elements of V. Elements of V are called vertices and elements of E are called edges. A graph is normally represented schematically as points and lines joining some of these points. The points are associated with vertices of a graph, whereas, lines joining pairs of points are associated with its edges. Figure 1.1 shows a graph with 5 vertices and 6 edges, with {1,2,3,4,5} being its vertex set and {{1,2}, {2,3}, {3,4}, {3,5}, {1,5}} being a family of its edges. The number of vertices in a graph is called the order of the graph.
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