Exercise 4: (a) Define eccentricity of the vertex and center of a graph. Find the center of the above graph. (b) List all cut-sets, cut-vertices if any, of the graph given above. (c) Show that with respect to the MCST by Kruskal's algorithm of the above connected graph with n vertices and e edges, the tree has (n-1) branches and (e- n + 1) chords. (d) Define fundamental circuits and fundamental cut sets. Find all possible fundamental circuits and fundamental cut sets with respect to the resulting MCST of applying Prim's algorithm. Exercise 4: (a) Define eccentricity of the vertex and center of a graph. Find the center of the above graph. (b) List all cut-sets, cut-vertices if any, of the graph given above. (c) Show that with respect to the MCST by Kruskal's algorithm of the above connected graph with n vertices and e edges, the tree has (n-1) branches and (e- n + 1) chords. (d) Define fundamental circuits and fundamental cut sets. Find all possible fundamental circuits and fundamental cut sets with respect to the resulting MCST of applying Prim's algorithm