A plane graph is a graph drawn on a plane so that no two edges of the graph (or the curves which represent them ) have a common point except a vertex which is incident on them both. Thus the notion of ‘plane graph’ refers to the graph image rather than to the graph itself. A graph is called planar (embeddable in the plane) if it can be drawn on a plane with no two edges crossing each other. The resultant planar graph image is called an embedding of the graph in the plane or a planar embedding. Figure 2.1 shows two planar graphs, only the second of which is plane.
KeywordsPlanar Graph Initial Graph Planar Embedding Virtual Edge Biconnected Graph
Unable to display preview. Download preview PDF.