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squaregraph
In graph theory, a branch of mathematics, a squaregraph is a type of undirected graph that can be drawn in the plane in such a way that every bounded face is a quadrilateral and every vertex with three or fewer neighbors is incident to an unbounded face.
==Related graph classes==
The squaregraphs include as special cases trees, grid graphs, gear graphs, and the graphs of polyominos.
As well as being planar graphs, squaregraphs are median graphs, meaning that for every three vertices ''u'', ''v'', and ''w'' there is a unique median vertex ''m''(''u'',''v'',''w'') that lies on shortest paths between each pair of the three vertices.〔. See for a discussion of planar median graphs more generally.〕 As with median graphs more generally, squaregraphs are also partial cubes: their vertices can be labeled with binary strings such that the Hamming distance between strings is equal to the shortest path distance between vertices.
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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