Editing Degree (graph theory) (section)

==Global properties==
*If each vertex of the graph has the same degree&nbsp;''k'', the graph is called a [[regular graph|''k''-regular graph]] and the graph itself is said to have degree&nbsp;''k''. Similarly, a [[bipartite graph]] in which every two vertices on the same side of the bipartition as each other have the same degree is called a [[biregular graph]].
*An undirected, connected graph has an [[Eulerian path]] if and only if it has either 0 or 2 vertices of odd degree. If it has 0 vertices of odd degree, the Eulerian path is an Eulerian circuit.
*A directed graph is a [[directed pseudoforest]] if and only if every vertex has outdegree at most&nbsp;1. A [[functional graph]] is a special case of a pseudoforest in which every vertex has outdegree exactly&nbsp;1.
*By [[Brooks' theorem]], any graph ''G'' other than a clique or an odd cycle has [[chromatic number]] at most&nbsp;Δ(''G''), and by [[Vizing's theorem]] any graph has [[chromatic index]] at most Δ(''G'')&nbsp;+&nbsp;1.
*A [[Degeneracy (graph theory)|''k''-degenerate graph]] is a graph in which each subgraph has a vertex of degree at most ''k''.