Given an undirected graph, a degree sequence is a monotonic nonincreasing sequence of the vertex degrees (valencies) of its graph vertices. The number of degree sequences for a graph of a given order is closely related to graphical partitions. The sum of the elements of a degree sequence of a graph is always even due to fact that each edge connects two vertices and is thus counted twice. The minimum vertex degree in a graph G is denoted δ(G), and the maximum vertex degree is denoted Δ(G). A graph whose degree sequence contains only multiple copies of a single integer is called a regular graph. A graph corresponding to a given degree sequence d can be constructed in the Wolfram Language using RandomGraph[DegreeGraphDistribution[d]].

degree set | graphical partition | graphic sequence | k-connected graph | regular graph | unigraphic graph | unswitchable graph | vertex degree