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Let $G_{C}=(V, M)$ be a graph with $V=\{a, b, c, d, e, f\}$ and $M$ is the set of edges represented by the following adjacency matrix:
Which of the following statements are true about the undirected version of $G_{C}$ ? Note that the undirected version of a directed graph is obtained by replacing every directed edge (if any) by its undirected version.
A. GC is 1-vertex connected.
B. GC is 2-vertex connected.
C. GC is 3-vertex connected.
D. GC is 4-vertex connected
E. GC is 1-edge connected.
F. GC is 2-edge connected.
G. GC is 3-edge connected.
H. GC is 4-edge connected.
1. None of the above.

Answer

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Answer

Thus, the correct statements are B and F, which means $G_C$ is 2-vertex connected and 2-edge connected. \(\boxed{\text{B, F}}\)

Steps

Step 1 :First, we need to find the adjacency matrix of the undirected version of $G_C$. To do this, we replace every directed edge with its undirected version.

Step 2 :Next, we analyze the graph to determine its vertex and edge connectivity.

Step 3 :Vertex connectivity is the minimum number of vertices that need to be removed to disconnect the graph. We can see that removing vertices $a$ and $b$ will disconnect the graph, so $G_C$ is 2-vertex connected.

Step 4 :Edge connectivity is the minimum number of edges that need to be removed to disconnect the graph. We can see that removing edges $(a, c)$ and $(b, c)$ will disconnect the graph, so $G_C$ is 2-edge connected.

Step 5 :Thus, the correct statements are B and F, which means $G_C$ is 2-vertex connected and 2-edge connected. \(\boxed{\text{B, F}}\)

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