<Li> If each vertex of the graph has the same degree k the graph is called a k - regular graph and the graph itself is said to have degree 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 . </Li> <Li> 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 . </Li> <Li> A directed graph is a pseudoforest if and only if every vertex has outdegree at most 1 . A functional graph is a special case of a pseudoforest in which every vertex has outdegree exactly 1 . </Li> <Li> By Brooks' theorem, any graph other than a clique or an odd cycle has chromatic number at most Δ, and by Vizing's theorem any graph has chromatic index at most Δ + 1 . </Li>

Maximum degree of any node in a simple graph with n vertices is