Question:
Choose the correct statement about connected components.
Choose the correct statement about connected components.
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Connected Component = Maximal Connected Subgraph.
Whenever a graph is disconnected, it can be partitioned into one or more connected components.
Updated On: Jun 25, 2026
- A connected component of a graph is a maximal connected subgraph of that graph
- A connected component of a graph is a Hamiltonian circuit
- A connected component of a graph may be Euler but not Hamiltonian
- A complete directed graph will not have connected component
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The Correct Option is A
Solution and Explanation
Concept:
A connected component is one of the fundamental concepts in graph theory.
It represents a maximal connected part of a graph.
The word "maximal" means that no additional vertex from the graph can be included while preserving connectedness.
Step 1: Define a connected graph.
A graph is connected if there exists a path between every pair of vertices. If a graph is not connected, it can be divided into several connected pieces.
Step 2: Define a connected component.
A connected component is a connected subgraph that cannot be enlarged by adding more vertices from the graph. Hence it is called a maximal connected subgraph.
Step 3: Examine the options.
Option (A) gives the exact definition. Option (B) describes a Hamiltonian circuit, which is unrelated. Option (C) is not a definition of connected components. Option (D) is false because directed graphs can also possess connected components.
Step 4: Write the conclusion.
Therefore, \[ \boxed{\text{A connected component is a maximal connected subgraph}} \] and option (A) is correct.
Step 1: Define a connected graph.
A graph is connected if there exists a path between every pair of vertices. If a graph is not connected, it can be divided into several connected pieces.
Step 2: Define a connected component.
A connected component is a connected subgraph that cannot be enlarged by adding more vertices from the graph. Hence it is called a maximal connected subgraph.
Step 3: Examine the options.
Option (A) gives the exact definition. Option (B) describes a Hamiltonian circuit, which is unrelated. Option (C) is not a definition of connected components. Option (D) is false because directed graphs can also possess connected components.
Step 4: Write the conclusion.
Therefore, \[ \boxed{\text{A connected component is a maximal connected subgraph}} \] and option (A) is correct.
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