In the following lab task you are required to modify the Graph.java in the folder LabTask$01$ such that it

represents a graph using adjacency matrix representation similar to the above representation.

Page $1$ of $4$

$($a$)$ Complete the method: public void addEdge$($int $i,$ int $j)$ to add an undirected edge $i-j$ to the graph.

Note: For an undirected graph, if an edge $i-j$ is added to the graph then the reverse edge $j-$ i must also

be added.

$($b$)$ Complete the method: public void removeEdge$($int $i,$ int $j)$ to remove an undirected edge $i-j$ from the

graph

Note: For an undirected graph, an edge $i-j$ is removed from the graph then the reverse edge $j-$i must

also be removed.

$($c$)$ Complete the method: public boolean isEdge$($int $i,$ int $j).$ The method returns true if $i-j$ is an undirected

edge in the graph; otherwise, it returns false.

$($d$)$ Complete the driver class by creating the following graph:

Run the program to get an output of the following form:

public class Graph $\{$

private boolean adjacencyMatrix$[][]$;

private int numberOfVertices;

public Graph$($int numberOfVertices$)\{$

this.numberOfVertices $=$ numberOfVertices;

adjacencyMatrix $=$ new boolean$[$numberOfVertices$][$numberOfVertices$]$;

$\}$

public void addEdge$($int i$,$ int j$)\{$

$//$ To be completed by students

$\}$

public void removeEdge$($int i$,$ int j$)\{$

$//$ To be completed by students

$\}$

public boolean isEdge$($int i$,$ int j$)\{$

$//$ to be completed by students

$\}$

public void displayGraph$()\{$

System.out.printf$("\%10$s$","")$;

for$($int i $=0$; i $$ numberOfVertices; i$++)$

System.out.printf$("\%10$s$",$ i$)$;

System.out.println$()$;

for$($int i $=0$; i $$ numberOfVertices; i$++)\{$

System.out.printf$("\%10$s$",$ i$)$;

for$($int j $=0$; j $$ numberOfVertices; j$++)\{$

System.out.printf$("\%10$s$",$ adjacencyMatrix$[$i$][$j$])$;

$\}$

System.out.println$()$;

$\}$

$\}$

$\}$

public class GraphDriver$\{$

public static void main$($String$[]$ args$)\{$

$//$ Create an undirected graph with $4$ vertices

$//$ To be completed by students

$//$ Add the $5$ edges of the graph

$//$ To be completed by students

$//$ Display the graph before deleting edge $2---3$

System.out.println$("$Before deleting edge $2---3$ the graph is:

$")$;

$//$ To be completed by students

$//$ Display the graph after deleting edge $2---3$

$//$ To be completed by students

System.out.println$("$

After deleting edge $2---3$ the graph is:

$")$;

$//$ To be completed by students

$\}$

$\}$