Knowlpedia

Definition

Vertex degree

The number of neighbors of a vertex in a simple undirected graph.

The degree of a vertex vv in a simple undirected G=(V,E)G=(V,E) is

deg⁡G(v)=∣{w∈V:{v,w}∈E}∣.\deg_G(v)=\bigl|\{w\in V:\{v,w\}\in E\}\bigr|.

It counts the neighbors of vv. The degree may be infinite.

Bounded degree

The graph has degree bounded by Δ\Delta if deg⁡G(v)≤Δ\deg_G(v)\le\Delta for every vertex, where Δ\Delta is a fixed nonnegative integer. A graph can have infinitely many vertices and bounded degree. Requiring each degree to be finite is weaker than requiring one finite bound for all vertices.