Draw the graph represented by the following adjacency matrix $[5$ MARKS$]$

$\backslash$table$[[,$a$,$b$,$c$,$d$,$e$,$f$,$g$],[$a$,,7,4,,,,,],[$b$,,,5,3,,,,],[$c$,,,,1,,,,],[$d$,,1,,,2,,,],[$e$,,1,,,,,,],[$f$,,,4,1,,,2,],[$g$,,,,,1,,,]]$

Draw the adjacency list representation for this graph.$[5$marks$]$

What is the sequence of vertices visited when we perform breadth$-$first search from a$?[10$ marks$]$

a$.$ Use Prim's algorithm starting at node A to compute the Minimum Spanning Tree $($MST$)$ of the following graph. In particular, write down the edges of the MST in the order in which Prim's algorithm adds them to the MST$.$ Use the format $($nodel; node$2)$ to denote an edge.$[8$ marks$]$