Question

A subgraph H of a graph G is called a clique if _______.

• A. \( V(G) = V(H) \)
• B. \( V(H) \subseteq V(G) \)
• C. \( H \) contains all edges of \( G \)
• D. \( H \) is also a complete graph

Hint:

In graph theory, a clique is a subset of a graph where every pair of vertices is connected by an edge. It must be a complete subgraph.

Answer 1

The Correct Option is D

A clique in a graph is a subgraph where every pair of distinct vertices is adjacent to each other. 
Therefore, a subgraph \( H \) of graph \( G \) is called a clique if \( H \) is a complete graph. In a complete graph, every vertex is connected to every other vertex. This is the defining characteristic of a clique. 
Therefore, option (4) is correct.