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Rotation map : ウィキペディア英語版
Rotation map

In mathematics, a rotation map is a function that represents an undirected edge-labeled graph, where each vertex enumerates its outgoing neighbors. Rotation maps were first introduced by Reingold, Vadhan and Wigderson (“Entropy waves, the zig-zag graph product, and new constant-degree expanders”, 2002) in order to conveniently define the zig-zag product and prove its properties.
Given a vertex v and an edge label i, the rotation map returns the i'th neighbor of v and the edge label that would lead back to v.
==Definition==
For a ''D''-regular graph ''G'', the rotation map \mathrm_G : () \times () \rightarrow () \times () is defined as follows: \mathrm_G (v,i)=(w,j) if the ''i''th edge leaving ''v'' leads to ''w'', and the ''j''th edge leaving ''w'' leads to ''v''.

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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