Graph (discrete mathematics): Difference between revisions

Revision as of 18:31, 27 June 2006

Revision as of 18:32, 27 June 2006

Line 47:

The term "[[multigraph]]" is used to indicate that multiple edges (and sometimes loops) are allowed. Where graphs are defined so as to ''allow'' loops and multiple edges, a multigraph is often defined to mean a graph without loops,<ref> For example, see Balakrishnan, p. 1, Gross (2003), p. 4, and Zwillinger, p. 220.</ref> however, where graphs are defined so as to ''disallow'' loops and mutiple edges, the term is often defined to mean a "graph" which can have loops or multiple edges.<ref>For example, see. Bollobas, p. 7, Diestel, p. 25, and Harary, p. 10.</ref>

Sometimes the term "[[pseudograph]]" is used to indicate that both multiple edges and loops are allowed.<ref>Gross (20051998), p. 3, and Zwillinger, p. 220.</ref> In exceptional situations it is even necessary to have edges with only one end, called '''halfedges''', or no ends ('''loose edges'''); see for example [[signed graph]]s.

==Properties of graphs==