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| Replacement product ： ウィキペディア英語版 |
Replacement product
In graph theory, the replacement product of two graphs is a graph product that can be used to reduce the degree of a graph while maintaining its connectivity.
Suppose ''G'' is a ''d''-regular graph and ''H'' is an ''e''-regular graph with vertex set . Let ''R'' denote the replacement product of ''G'' and ''H''. The vertex set of ''R'' is the Cartesian product ''V''(''G'') × ''V''(''H''). For each vertex ''u'' in ''V''(''G'') and for each edge (''i'', ''j'') in ''E''(''H''), the vertex (''u'', ''i'') is adjacent to (''u'', ''j'') in ''R''. Furthermore, for each edge (''u'', ''v'') in ''E''(''G''), if ''v'' is the ''i''th neighbor of ''u'' and ''u'' is the ''j''th neighbor of ''v'', the vertex (''u'', ''i'') is adjacent to (''v'', ''j'') in ''R''.
If ''H'' is an ''e''-regular graph, then ''R'' is an (''e'' + 1)-regular graph.
== References ==
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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