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A clique in a undirected graph \(G = V,E\) is a subset V’ ⊆ V of vertices, such that

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UGC NET Computer Science (Paper 2) Dec 2019 Paper
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  1. If (u, v) ∈ E then u ∈ V’ and v ∈ V’
  2. If (u, v) ∈ E then u ∈ V’ or v ∈ 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

Answer (Detailed Solution Below)

Option 3 : Each pair of vertices in V’ is connected by an edge
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Detailed Solution

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Concept:

A clique is a subset of vertices of an undirected graph G such that every two distinct vertices in the clique are adjacent.

Explanation:

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. 

F1 R.S 1.6.20 Pallavi D3

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