Question 7 Choose the best option based on following statements i) A graph is said to be...
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Choose the best option based on following statements
i) A graph is said to be complete if there is no edge between every pair of vertices.
ii) An undirected graph which contains no cycles is called a forest.
iii) Network is a graph that has weights or costs associated with it.
Show answer & explanation
Statement i is False because a complete graph has an edge between every pair of vertices. Statement ii is True (acyclic undirected graph is a forest). Statement iii is True (a network is a weighted graph).
Step-by-step Derivation:
Step 1: Statement (i): A complete graph connects all pairs of vertices. Stating there is 'no edge' is False.
Step 2: Statement (ii): A forest is an undirected graph with no cycles. True.
Step 3: Statement (iii): A graph with weights or costs is termed a network. True.
Step 4: Result: False, True, True.