odd graph
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Input interpretation

odd graph

Definition

The odd graph O_n of order n is a graph having vertices given by the (n - 1)-subsets of {1, ..., 2n - 1} such that two vertices are connected by an edge iff the associated subsets are disjoint (Biggs 1993, Ex. 8f, p. 58). Some care is needed since the convention of defining the odd graph based on the n-subsets of {1, ..., 2n + 1} is sometimes also used, leading to a shifting of the index by one (e.g., West 2000, Ex. 1.1.28, p. 17).
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Related terms

complete graph | distance-regular graph | distance-transitive graph | Kneser graph | odd vertex | Petersen graph

Related Wolfram Language symbols

Entity | FromEntity | GraphData

Subject classifications

MathWorld

biconnected graphs | bridgeless graphs | connected graphs | cyclic graphs | distance-regular graphs | distance-transitive graphs | edge-transitive graphs | integral graphs | Kneser graphs | odd graphs | regular graphs | square-free graphs | symmetric graphs | traceable graphs | vertex-transitive graphs

MSC 2010

05Cxx
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