Complete graph
A complete graph is a type of graph where every pair of vertices has a direct edge connecting them. In other words, in a complete graph, you can get from any vertex to any other vertex in just one step.
Complete graph: a graph where every pair of vertices is directly connected by an edge.
Notation
Section titled “Notation”A complete graph with n vertices is often written as
is a complete graph with 3 vertices, where each vertex is connected to the other two vertices. is a complete graph with 4 vertices, where each vertex is connected to the other three vertices.
Number of edges
Section titled “Number of edges”In a complete graph with
This assumes the graph is undirected.
Number of hamiltonian cycles
Section titled “Number of hamiltonian cycles”For a complete graph with