Vertex Degree
The degree deg(v) of vertex v is the number of edges incident on v or equivalently, deg(v) = |N(v)|. The degree sequence of graph is (deg(v1), deg(v2), ..., deg(vn)), typically written in nondecreasing or nonincreasing order. The minimum and maximum degree of vertices in V(G) are denoted by d(G) and ∆(G), respectively. If d(G) = ∆(G) = r, then graph G is said to be regular of degree r, or simply r-regular.
Formally, given a graph G = (V, E), the degree of a vertex v Î V is the number of its neighbors in the graph. That is,
deg(v) = | {u Î V : (v, w) Î E}|.
If G is directed, we distinguish between in-degree (nimber of incoming neighbors) and out-degree (number of outgoing neighbors) of a vertex.
The degree deg(v) of vertex v is the number of edges incident on v or equivalently, deg(v) = |N(v)|. The degree sequence of graph is (deg(v1), deg(v2), ..., deg(vn)), typically written in nondecreasing or nonincreasing order. The minimum and maximum degree of vertices in V(G) are denoted by d(G) and ∆(G), respectively. If d(G) = ∆(G) = r, then graph G is said to be regular of degree r, or simply r-regular.
Formally, given a graph G = (V, E), the degree of a vertex v Î V is the number of its neighbors in the graph. That is,
deg(v) = | {u Î V : (v, w) Î E}|.
If G is directed, we distinguish between in-degree (nimber of incoming neighbors) and out-degree (number of outgoing neighbors) of a vertex.