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Outerplanar graph
In graph theory, an undirected graph is an outerplanar graph if it can be drawn in the plane without crossings in such a way that all of the vertices belong to the unbounded face of the drawing. That is, no vertex is totally surrounded by edges. Alternatively, a graph ''G'' is outerplanar if the graph formed from ''G'' by adding a new vertex, with edges connecting it to all the other vertices, is a planar graph.〔.〕
A maximal outerplanar graph is an outerplanar graph that cannot have any additional edges added to it while preserving outerplanarity. Every maximal outerplanar graph with ''n'' vertices has exactly 2''n'' − 3 edges, and every bounded face of a maximal outerplanar graph is a triangle.
==History==
Outerplanar graphs were first studied and named by , in connection with the problem of determining the planarity of graphs formed by using a perfect matching to connect two copies of a base graph (for instance, many of the generalized Petersen graphs are formed in this way from two copies of a cycle graph). As they showed, when the base graph is biconnected, a graph constructed in this way is planar if and only if its base graph is outerplanar and the matching forms a dihedral permutation of its outer cycle.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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