Английская Википедия:Bouquet graph

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Файл:Topological Rose.png

<math>B_4</math>, a bouquet with one vertex and four self-loop edges

In mathematics, a bouquet graph <math>B_m</math>, for an integer parameter <math>m</math>, is an undirected graph with one vertex and <math>m</math> edges, all of which are self-loops. It is the graph-theoretic analogue of the topological bouquet, a space of <math>m</math> circles joined at a point. When the context of graph theory is clear, it can be called more simply a bouquet.Шаблон:R

Файл:Self-trial ribbon graph.svg

Ribbon graph representation of an embedding of <math>B_3</math> onto the projective plane.

Although bouquets have a very simple structure as graphs, they are of some importance in topological graph theory because their graph embeddings can still be non-trivial. In particular, every cellularly embedded graph can be reduced to an embedded bouquet by a partial duality applied to the edges of any spanning tree of the graph,Шаблон:R or alternatively by contracting the edges of any spanning tree.

In graph-theoretic approaches to group theory, every Cayley–Serre graph (a variant of Cayley graphs with doubled edges) can be represented as the covering graph of a bouquet.Шаблон:R

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Шаблон:Graph-stub