Some graphs are used more than others, and get special names.

\(K_n\): The complete graph on \(n\) vertices.
\(K_{m,n}\): The complete bipartite graph with sets of \(m\) and \(n\) vertices.
\(C_n\): The cycle on \(n\) vertices, just one big loop.
\(P_n\): The path on \(n+1\) vertices (so \(n\) edges), just one long path.