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odd graph
In the mathematical field of graph theory, the odd graphs ''On'' are a family of symmetric graphs with high odd girth, defined from certain set systems. They include and generalize the Petersen graph.
==Definition and examples==
The odd graph ''On'' has one vertex for each of the (''n'' − 1)-element subsets of a (2''n'' − 1)-element set. Two vertices are connected by an edge if and only if the corresponding subsets are disjoint. That is, ''On'' is a Kneser graph ''KG''(2''n'' − 1,''n'' − 1).
''O''2 is a triangle, while ''O''3 is the familiar Petersen graph.
The generalized odd graphs include the odd graphs and the folded cube graphs, and are defined as distance-regular graphs with diameter ''n'' − 1 and odd girth 2''n'' − 1 for some ''n''.〔
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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