Star

Definition

A star is a graph where one vertex is adjacent to all the other vertices, and that vertex is incident on every edge. Explicitly, a star with $k$ edges (and therefore, $k+1$ vertices) is a graph where one of the $k+1$ vertices is adjacent to all other $k$ vertices, and there are no edges other than the edges involving that vertex.

A star can also be described as a complete bipartite graph where one of the parts has size one. Explicitly, a star with $k$ edges can be described as the complete bipartite graph $K_{1,k}$.