Answer all of the question. Marks for each question is indicated on the right side

a$.$ Construct an adjacency matrix for the following graph:

$3$

$2$

b$.$ Define weighted graph and connected graph.

$2$ a$.$ Starting at vertex A and print the vertices in the order they are processed by DFS$.$ Assume the adjacency lists are in lexicographic order, e$.$g$.,$ when exploring vertex $x,$ the algorithm considers the edge $x$A before $xB.$

$4$

$\backslash$table$[[A,,,,,,]]$

b$.$ Find the discovery and finishing time of each vertex and draw the DFS tree

$4$

c$.$ Find the shortest path from $A$ to $G$ using the BFS algorithm for the graph of question $2.$a$.$ You have to provide a proper explanation.

answer all the questions.