Question $2$

$2($a$)$ Computing students must complete a capstone project during their final year of study. Please create a bipartite graph based on the information provided below, with one set of vertices representing the students and the other representing the available capstone projects. Connect the students to the projects using edges that reflect their interests. $(5$ marks$)$

$2($b$)$ Determine the student$-$project match using an appropriate maximum flow algorithm $($such as the Ford$-$Fulkerson or Edmonds$-$Karp algorithm$).$ Ensure that each student is paired with only one project, and that each project is assigned to only one student. $(10$ marks$)$

Hint: consider the edge weights as $1.$