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Shannon multigraph : ウィキペディア英語版
Shannon multigraph
__NOTOC__
In the mathematical discipline of graph theory, Shannon multigraphs, named after Claude Shannon by , are a special type of triangle graphs, which are used in the field of edge coloring in particular.
:''A Shannon multigraph is multigraph with 3 vertices for which either of the following conditions holds:''
:
*''a) all 3 vertices are connected by the same number of edges.''
:
*''b) as in a) and one additional edge is added.''
More precisely one speaks of Shannon multigraph , if the three vertices are connected by \left\lfloor \frac \right\rfloor , \left\lfloor \frac \right\rfloor and \left\lfloor \frac \right\rfloor edges respectively. This multigraph has maximum degree . Its multiplicity (the maximum number of edges in a set of edges that all have the same endpoints) is \left\lfloor \frac \right\rfloor .
==Examples==

File:Shannon multigraph 2.svg|Sh(2)
File:Shannon multigraph 3.svg|Sh(3)
File:Shannon multigraph 4.svg|Sh(4)
File:Shannon multigraph 5.svg|Sh(5)
File:Shannon multigraph 6.svg|Sh(6)
File:Shannon multigraph 7.svg|Sh(7)


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Shannon multigraph」の詳細全文を読む



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