“Multiple edges”的意思、由来-开放百科全书

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Multiple edges

释义

Notes
References

In graph theory, multiple edges (also called parallel edges or a multi-edge), are two or more edges that are incident to the same two vertices. A simple graph has no multiple edges.

Depending on the context, a graph may be defined so as to either allow or disallow the presence of multiple edges (often in concert with allowing or disallowing loops):

Where graphs are defined so as to allow multiple edges and loops, a graph without loops is often called a multigraph.^[1]
Where graphs are defined so as to disallow multiple edges and loops, a multigraph or a pseudograph is often defined to mean a "graph" which can have loops and multiple edges.^[2]

Multiple edges are, for example, useful in the consideration of electrical networks, from a graph theoretical point of view.^[3] Additionally, they constitute the core differentiating feature of multidimensional networks.

A planar graph remains planar if an edge is added between two vertices already joined by an edge; thus, adding multiple edges preserves planarity.^[4]

A dipole graph is a graph with two vertices, in which all edges are parallel to each other.

Notes

1. ^For example, see Balakrishnan, p. 1, and Gross (2003), p. 4, Zwillinger, p. 220.
2. ^For example, see Bollobás, [https://books.google.com/books?id=SbZKSZ-1qrwC&pg=PA7 p. 7]; Diestel, [https://books.google.com/books?id=aR2TMYQr2CMC&pg=PA28 p. 28]; Harary, p. 10.
3. ^Bollobás, [https://books.google.com/books?id=SbZKSZ-1qrwC&pg=PA39 pp. 39–40].
4. ^Gross (1998), [https://books.google.com/books?id=CRDMgj-DfdEC&pg=PA308 p. 308].

References

Balakrishnan, V. K.; Graph Theory, McGraw-Hill; 1 edition (February 1, 1997). {{isbn|0-07-005489-4}}.
Bollobás, Béla; Modern Graph Theory, Springer; 1st edition (August 12, 2002). {{isbn|0-387-98488-7}}.
Diestel, Reinhard; Graph Theory, Springer; 2nd edition (February 18, 2000). {{isbn|0-387-98976-5}}.
Gross, Jonathon L, and Yellen, Jay; Graph Theory and Its Applications, CRC Press (December 30, 1998). {{isbn|0-8493-3982-0}}.
Gross, Jonathon L, and Yellen, Jay; (eds); Handbook of Graph Theory. CRC (December 29, 2003). {{isbn|1-58488-090-2}}.
Zwillinger, Daniel; CRC Standard Mathematical Tables and Formulae, Chapman & Hall/CRC; 31st edition (November 27, 2002). {{isbn|1-58488-291-3}}.

1 : Graph theory objects

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