Named Graphs.

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.

$The graph K5: five vertices arranged in a pentagon. Each vertex is connected to each other vertex by an edge.$

$The graph K2,3: a row of two vertices on top and three on bottom. Each vertex in the top row is connected to each vertex on the bottom row.$

$The graph C6: a cycle of six vertices connected by six edges arranged as a hexagon.$

$The graph P5: six vertices connected by five edges. The first and last vertex have one edge, each other vertex has two edges (connecting to the previous and next vertex on the path).$