$1.$Consider the following graph:

a$)$Starting from node $\text{'}$B$\text{'},$ traverse this graph using Breadth$-$First Search $($BFS$).$ Record the order in which the nodes will be visited. In cases of multiple choices, select the nodes in alphabetical order $($i$.$e$.,$ ascending order$).$ Utilize a queue data structure and illustrate how the content of this queue changes step by step.

$(2$ Marks$)$

b$)$Starting from node $\text{'}$I$\text{'},$ conduct a Depth$-$First Search $($DFS$)$ traversal of this graph. Document the sequence in which the nodes will be visited. In instances of multiple choices, prioritize nodes in reverse alphabetical order, i$.$e$.,$ descending order. Employ a stack data structure and elucidate the evolution of the stack's content, outlining each step.

$(2$ Marks$)$

c$)$Begin at node $\text{'}$H$\text{'}$ and perform an Iterative Deepening Search $($IDS$)$ up to a depth of three. Illustrate the incremental expansion of the tree at each depth. When faced with multiple choices, prioritize the selection of nodes in alphabetical order $($i$.$e$.,$ ascending order$).$

$(2$ Marks$)$

d$)$Consider the graph above as a representation of the connections between various cities in a country. Explore the potential advantages of employing an intelligent agent in practical scenarios to identify optimal routes from a given source city to a destination city. Additionally, discuss the algorithms that could be well$-$suited for this specific purpose.

$(2$ Marks$)$