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In a connected graph, a bridge is an edge whose removal disconnects a graph. Which one of the following statements is True?
- a)A tree has no bridge
- b)A bridge cannot be part of a simple cycle
- c)Every edge of a clique with size ≥ 3 is a bridge (A clique is any complete subgraph of a graph)
- d)A graph with bridges cannot have a cycle
Correct answer is option 'B'. Can you explain this answer?
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In a connected graph, a bridge is an edge whose removal disconnects a ...
A bridge in a graph cannot be a part of cycle as removing it will not create a disconnected graph if there is a cycle.
Most Upvoted Answer
In a connected graph, a bridge is an edge whose removal disconnects a ...
Explanation:
To determine which statement is true, let's analyze each option one by one.
a) A tree has no bridge:
This statement is false. A tree can have bridges. In a tree, every edge is a bridge except for the edges that are part of a cycle. Removing any edge from a tree will disconnect it.
b) A bridge cannot be part of a simple cycle:
This statement is true. A bridge is defined as an edge whose removal disconnects the graph. If a bridge is part of a simple cycle, then it means that there is an alternative path between the two vertices connected by the bridge. Therefore, removing the bridge will not disconnect the graph, making it not a bridge.
c) Every edge of a clique with size 3 is a bridge (A clique is any complete subgraph of a graph):
This statement is false. In a clique of size 3, removing any edge will not disconnect the graph. The remaining two edges will still form a complete subgraph, and there will be a path between any two vertices.
d) A graph with bridges cannot have a cycle:
This statement is false. A graph with bridges can still have cycles. Bridges are edges that, when removed, disconnect the graph. However, removing a bridge does not necessarily remove all cycles from the graph. There can still be other paths that form cycles even after removing the bridges.
Therefore, the correct statement is b) A bridge cannot be part of a simple cycle, as explained above.
To determine which statement is true, let's analyze each option one by one.
a) A tree has no bridge:
This statement is false. A tree can have bridges. In a tree, every edge is a bridge except for the edges that are part of a cycle. Removing any edge from a tree will disconnect it.
b) A bridge cannot be part of a simple cycle:
This statement is true. A bridge is defined as an edge whose removal disconnects the graph. If a bridge is part of a simple cycle, then it means that there is an alternative path between the two vertices connected by the bridge. Therefore, removing the bridge will not disconnect the graph, making it not a bridge.
c) Every edge of a clique with size 3 is a bridge (A clique is any complete subgraph of a graph):
This statement is false. In a clique of size 3, removing any edge will not disconnect the graph. The remaining two edges will still form a complete subgraph, and there will be a path between any two vertices.
d) A graph with bridges cannot have a cycle:
This statement is false. A graph with bridges can still have cycles. Bridges are edges that, when removed, disconnect the graph. However, removing a bridge does not necessarily remove all cycles from the graph. There can still be other paths that form cycles even after removing the bridges.
Therefore, the correct statement is b) A bridge cannot be part of a simple cycle, as explained above.
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In a connected graph, a bridge is an edge whose removal disconnects a graph. Which one of the following statements is True?a)A tree has no bridgeb)A bridge cannot be part of a simple cyclec)Every edge of a clique with size ≥ 3 is a bridge (A clique is any complete subgraph of a graph)d)A graph with bridges cannot have a cycleCorrect answer is option 'B'. Can you explain this answer?
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