“Bouquet graph”的意思、由来-开放百科全书

In mathematics, a bouquet graph

, for an integer parameter

, is an undirected graph with one vertex and

edges, all of which are self-loops. It is the graph-theoretic analogue of the topological bouquet, a space of

circles joined at a point. When the context of graph theory is clear, it can be called more simply a bouquet.{{r|bw}}

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,{{r|em}} 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.{{r|s}}

References

1. ^{{citation | last1 = Ellis-Monaghan | first1 = Joanna A. | author1-link = Jo Ellis-Monaghan | last2 = Moffatt | first2 = Iain | issue = 3 | journal = Transactions of the American Mathematical Society | mr = 2869185 | pages = 1529–1569 | title = Twisted duality for embedded graphs | doi = 10.1090/S0002-9947-2011-05529-7 | volume = 364 | year = 2012| arxiv = 0906.5557}}
2. ^{{citation | last = Sunada | first = Toshikazu | doi = 10.1007/978-4-431-54177-6 | isbn = 978-4-431-54176-9 | mr = 3014418 | page = 69 | publisher = Springer, Tokyo | series = Surveys and Tutorials in the Applied Mathematical Sciences | title = Topological Crystallography: With a View Towards Discrete Geometric Analysis | url = https://books.google.com/books?id=6cNEAAAAQBAJ&pg=PA69 | volume = 6 | year = 2013}}