Editing Glossary of graph theory (section)

==G==
{{glossary}}

{{term|G|''G''}}
{{defn|A variable often used to denote a graph.}}

{{term|genus}}
{{defn|The genus of a graph is the minimum genus of a surface onto which it can be embedded; see {{gli|embedding}}.}}

{{term|geodesic}}
{{defn|As a noun, a geodesic is a synonym for a [[shortest path]]. When used as an adjective, it means related to shortest paths or shortest path distances.}}

{{term|giant}}
{{defn|In the theory of [[random graph]]s, a giant component is a connected component that contains a constant fraction of the vertices of the graph. In standard models of random graphs, there is typically at most one giant component.}}

{{term|girth}}
{{defn|The [[Girth (graph theory)|girth]] of a graph is the length of its shortest cycle.}}

{{term|graph}}
{{defn|The fundamental object of study in graph theory, a system of vertices connected in pairs by edges. Often subdivided into [[directed graph]]s or [[undirected graph]]s according to whether the edges have an orientation or not. [[Mixed graph]]s include both types of edges.}}

{{term|greedy}}
{{defn|Produced by a [[greedy algorithm]]. For instance, a [[greedy coloring]] of a graph is a coloring produced by considering the vertices in some sequence and assigning each vertex the first available color.}}

{{term|Grötzsch}}
{{defn|no=1|[[Herbert Grötzsch]]}}
{{defn|no=2|The [[Grötzsch graph]], the smallest triangle-free graph requiring four colors in any proper coloring.}}
{{defn|no=3|[[Grötzsch's theorem]] that triangle-free planar graphs can always be colored with at most three colors.}}

{{term|Grundy number}}
{{defn|no=1|The [[Grundy number]] of a graph is the maximum number of colors produced by a [[greedy coloring]], with a badly-chosen vertex ordering.}}

{{glossary end}}