In a connected graph, a bridge is an edge whose removal disconnects the graph. Which one of the following statements is true?
In a tree every edge is a BRIDGE
A helpful video to understand about clique What is a Clique? | Graph Theory, Cliques - YouTube
Bridge / cut edge : A single edge whose removal will disconnect the graph is known as Bridge or cut edge.
Correct Answer: $B$
A clique, C, in an undirected graph G = (V, E) is a subset of the vertices, C ⊆ V, such that every two distinct vertices are adjacent. This is equivalent to the condition that the induced subgraph of G induced by C is a complete graph. In some cases, the term clique may also refer to the subgraph directly.
So it cant be disconnect the graph
Answer: (B) Explanation: 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.
Bridge / cut edge :A single edge whose removal will disconnect the graph is known as Bridge or cut edge .
Cut set: It is a set of edges whose removal makes the graph disconnected.
The option (c) is wrong because they are asking for Bridge not cut set .Don't confuse with the definition.
@Hemant ,Yes u r right.
@Warrior 1st statement should be like this:- In a tree, every edge is cut edge and every vertex need not be a cut vertex.
@Warrior
If a tree has only left or right subtree (but not both) then root and leaves are not the cut vertex.
I didn’t get it. Anyone plz explain.
Since, every edge in a tree is bridge ∴ (A) is false Since, every edge in a complete graph kn(n≥3) is not a bridge ⇒ (C) is false Let us consider the following graph G: This graph has a bridge i.e., edge ‘e’ and a cycle of length ‘3’ ∴ (D) is false Since, in a cycle every edge is not a bridge ∴ (B) is true
@keshore muralidharan
Since, in a cycle every edge is not a bridge.
In a cycle, every edge is not a bridge → there exists at least one edge in a cycle which is not a bridge.
But, the statement should be like “ None of the edges in a cycle is a bridge”.
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