Miles Work Assig Q $\times$ Final Copy Induc MATH is par the 0 s/112858/quizzes/575154/take/questions/4552018 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.
Solution
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. \(\boxed{\text{B, F}}\)
