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By Danail Bonchev; Dennis H Rouvray

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A graph is called bipartite if adjacent vertices always have different colours when two different colours are used for colouring the vertices. It can be shown that bipartite graphs do not contain cycles of odd length; this requirement is a necessary and sufficient condition for bipartite graphs. 2*3 Connectedness of Graphs A graph G is called connected if for each pair of vertices {r, i} E (7 at least one path tør* exists; otherwise (? is a disconnected graph. Any connected part ft of a disconnected graph is called a component of G and, obviously, G — U ft- Therefore, a connected graph can be fi) designated as a single component graph.

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