Editing Glossary of graph theory (section)

==O==
{{glossary}}

{{term|odd}}
{{defn|no=1|An odd cycle is a cycle whose length is odd. The [[Girth (graph theory)|odd girth]] of a non-bipartite graph is the length of its shortest odd cycle. An odd hole is a special case of an odd cycle: one that is induced and has four or more vertices.}}
{{defn|no=2|An odd vertex is a vertex whose degree is odd. By the [[handshaking lemma]] every finite undirected graph has an even number of odd vertices.}}
{{defn|no=3|An odd ear is a simple path or simple cycle with an odd number of edges, used in odd ear decompositions of factor-critical graphs; see {{gli|ear}}.}}
{{defn|no=4|An odd chord is an edge connecting two vertices that are an odd distance apart in an even cycle. Odd chords are used to define [[strongly chordal graph]]s.}}
{{defn|no=5|An [[odd graph]] is a special case of a [[Kneser graph]], having one vertex for each {{math|(''n'' &minus; 1)}}-element subset of a {{math|(2''n'' &minus; 1)}}-element set, and an edge connecting two subsets when their corresponding sets are disjoint.}}

{{term|open}}
{{defn|no=1|See {{gli|neighbourhood}}.}}
{{defn|no=2|See {{gli|walk}}.}}

{{term|order|content ={{vanchor|order}} }}
{{defn|no=1|The order of a graph {{mvar|G}} is the number of its vertices, {{math|{{!}}''V''(''G''){{!}}}}. The variable {{mvar|n}} is often used for this quantity. See also {{gli|size}}, the number of edges.}}
{{defn|no=2|A type of [[logic of graphs]]; see {{gli|first order}} and {{gli|second order}}.}}
{{defn|no=3|An order or ordering of a graph is an arrangement of its vertices into a sequence, especially in the context of [[topological ordering]] (an order of a directed acyclic graph in which every edge goes from an earlier vertex to a later vertex in the order) and [[degeneracy (graph theory)|degeneracy ordering]] (an order in which each vertex has minimum degree in the induced subgraph of it and all later vertices).}}
{{defn|no=4|For the order of a haven or bramble, see {{gli|haven}} and {{gli|bramble}}.}}

{{term|orientation}}
{{term|oriented|multi=y}}
{{defn|no=1|An [[Orientation (graph theory)|orientation]] of an undirected graph is an assignment of directions to its edges, making it into a directed graph. An oriented graph is one that has been assigned an orientation. So, for instance, a [[polytree]] is an oriented tree; it differs from a directed tree (an arborescence) in that there is no requirement of consistency in the directions of its edges. Other special types of orientation include [[Tournament (graph theory)|tournaments]], orientations of complete graphs; [[strong orientation]]s, orientations that are strongly connected; [[acyclic orientation]]s, orientations that are acyclic; [[Eulerian path|Eulerian orientation]]s, orientations that are Eulerian; and [[transitive orientation]]s, orientations that are transitively closed.}}
{{defn|no=2|Oriented graph, used by some authors as a synonym for a [[directed graph]].}}

{{term|out-degree}}
{{defn|See {{gli|degree}}.}}

{{term|outer}}
{{defn|See {{gli|face}}.}}

{{term|outerplanar}}
{{defn|An [[outerplanar graph]] is a graph that can be embedded in the plane (without crossings) so that all vertices are on the outer face of the graph.}}

{{glossary end}}