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

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

$2$

b$.$ Consider A graph $G$ with vertices $(1,2,3,4\}$ and edges $,(4,1),(2,1),(2,4).$ For every vertex $u,$ find its indegree in $(u)$ and its outdegree out $(u).$ What is the value of the following Sum for this graph?

${\displaystyle \underset{\text{u}\text{i}\text{n}\text{v}}{\overset{?}{}}}in(u)+$ out $(u)=$

$3$

c$.$ In the following graphs, assume that if there is ever a choice amongst multiple nodes, both the BFS and DFS algorithms will choose the left$-$most node first.

$A^{\text{'}}{B}^{\text{'}}C$

$2$

Starting from the node $S$ at the top, which algorithm will visit the least number of nodes before visiting the goal node $G?$ Breadth First Search, Depth First Search, or both Algorithm will encounter the same number of nodes? Explain.

$2.$ a$.$ Apply DFS and show the discovery and finishing time of each node considering the source node is $B$