Definition:Complete Graph

Definition
Let $G = \left({V, E}\right)$ be a simple graph such that every vertex is adjacent to every other vertex.

Then $G$ is called complete.

The complete graph of order $p$ is denoted $K_p$.

Also see

 * $K_p$ is $p - 1$-regular
 * Complete Graph of Order 1 is Edgeless


 * $K_n$ is Hamiltonian for all $n \ge 3$, from Ore's Theorem or trivially, by inspection.


 * $K_1$ is the path graph $P_1$.


 * $K_2$ is the path graph $P_2$, and also the complete bipartite graph $K_{1, 1}$.


 * $K_3$ is the cycle graph $C_3$, and is also called a triangle.


 * $K_4$ is the graph of the tetrahedron.


 * Complement of Complete Graph is Edgeless Graph