Regular Graph

• A regular graph is a graph where the degree of each vertex in the graph is equal. If each vertex has degree , then the graph is -regular.

  More formally, if is the -regular graph then

• A -factor of a graph is a spanning -regular subgraph. A -factorization partitions the edges of a graph into disjoint -factors.

  • A -factor is a perfect matching.
  • A -factorization of a -regular graph is a proper edge coloring.

Families §

• Cubic Graph - a -regular graph.
• Cycles - a connected -regular graphs
• Vertex Transitive Graph
• Cayley Digraph