Graph (discrete mathematics): Difference between revisions

Revision as of 16:36, 29 October 2024

Revision as of 11:14, 31 October 2024

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=== Directed graph ===

{{main|Directed graph}}

[[File:Directed.svg|thumb|upright|A directed graph with three vertices and four directed edges, where (the double arrow represents antwo directed edgeedges in eachopposite direction.)]]

A '''directed graph''' or '''digraph''' is a graph in which edges have orientations.

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=== Mixed graph ===

{{main|Mixed graph}}

[[File:Example of simple mixed graph.jpg|thumb|upright|A simple mixed graph with three vertices, two directed edges, and an undirected edge.]]

A ''mixed graph'' is a graph in which some edges may be directed and some may be undirected. It is an ordered triple {{math|1=''G'' = (''V'', ''E'', ''A'')}} for a ''mixed simple graph'' and {{math|1=''G'' = (''V'', ''E'', ''A'', ''ϕ{{sub|E}}'', ''ϕ{{sub|A}}'')}} for a ''mixed multigraph'' with {{mvar|V}}, {{mvar|E}} (the undirected edges), {{mvar|A}} (the directed edges), {{mvar|ϕ{{sub|E}}}} and {{mvar|ϕ{{sub|A}}}} defined as above. Directed and undirected graphs are special cases.