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A clique in an undirected graph $G= \left \langle V, E \right \rangle$ is a subset $V’ \subseteq V$ of vertices, such that

  1. If $(u,v) \in E$ then $u \in V’$ and $v \in V’$
  2. If $(u,v) \in E$ then $u \in V’$ or $v \in V’$
  3. Each pair of vertices in $V’$ is connected by an edge
  4. All pairs of vertices in $V’$ are not connected by an edge
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A clique in an undirected graph G = (V, E) is a subset of V i.e. V’ such that each pair of vertices in V’
is connected by an edge. A clique of size k is called k- clique. A 0- clique contains set of 0 vertices.
A maximal clique is a clique that cannot be extended by including one more adjacent vertex. A
maximum clique of G is such that there is no clique with more vertices.

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