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In mathematics, a bouquet graph B m {\displaystyle B_{m}} , for an integer parameter m {\displaystyle m} , is an undirected graph with one vertex and m {\displaystyle m} edges, all of which are self-loops. It is the graph-theoretic analogue of the topological bouquet, a space of m {\displaystyle m} circles joined at a point. When the context of graph theory is clear, it can be called more simply a bouquet.
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, or alternatively by contracting the edges of any spanning tree.
In graph-theoretic approaches to group theory, every Cayley–Serre graph can be represented as the covering graph of a bouquet.