Question

question 9 of 10 (1 point) | question attempt: 1 of unlimited
if there are no bridges, select
one\.
c, j
the graph is disconnected.
(b)
the graph is connected.
list all the bridges.
if there are no bridges, select
one\.
the graph is disconnected.

Explanation:

Step1: Recall the definition of a bridge

A bridge in a graph is an edge whose removal increases the number of connected components.

Step2: Analyze the graph

Looking at the graph with vertices \(P, Q, R, S, T, U, V, W, X, Y\). If we consider each edge:

• For the sub - graph \(U - R - S - Y\) and \(U - V - W - X - Y\), if we remove any non - bridge edge, the graph remains connected. But for the edge \(R - U\):
• If we remove the edge \(R - U\), the part of the graph containing \(V, W, X, Y\) (connected through \(S - Y\) and \(W - X - Y\)) and the part containing \(P, Q, R, S, T\) (connected through \(Q - R - S - T\) and \(P - Q, P - T\)) would still be connected.
• For the edge \(S - Y\):
• If we remove \(S - Y\), the graph is still connected. The vertices \(U, V, W, X, Y\) are connected (\(U - R - S - T\) part is connected in another way).
• For the edge \(P - Q\):
• Removing \(P - Q\) leaves the graph connected (\(P - T - S - R - Q\) path still exists).
• For the edge \(P - T\):
• Removing \(P - T\) leaves the graph connected (\(P - Q - R - S - T\) path still exists).
• After checking all edges, we find that there is no edge whose removal will disconnect the graph.

Answer:

None