graph theory:
    Complete graph is graph where each vertex is connected with all other vertices (usually) by one edge. More formal: if all the vertices of graph G=(V, E) are pairwise adjacent edges, then graph G is complete graph.
    
    Complete graph on n vertices is denoted `K^n` or `K_n`.
    
    If two complete graphs have the same number of vertices, then they are isomorphic graphs. `K_(n+1)` is isomorphic to the suspension of the complete graph `K_n` from the `K_1`.
    
    `K_n` is a Cayley graph. The edge-complement of `K_n` has no edges and n vertices: `(K_n)^c`= (V, `O/`).
    
    Every vertex in `K_n` has a neighborhood isomorphic to `K_(n-1)`.
    
    `K_1` is a single vertex with no edges, sometimes called the trivial graph.
    
    `K_2` is an one edge connecting two vertices:
    
    

    Complete graph on 3 vertices is called triangle.
    `K_3`:
    
    
    `K_4`:
    
    
    `K_5`: