Please help me solve this. Please add test cases showing the program works as intended.The fourth programming project involves writing a program that allows the user to create an

undirected graph that is visually displayed and to check whether the graph is connected and

whether it has cycles in response to button clicks. In addition, it should provide buttons, when

clicked, display a depth$-$first or breadth$-$first graph search. The GUI for the program is shown

below:

The user should be able to add vertices to the graph by left elicking the mouse at the desired

location. The first vertex created should be labeled A and subsequent vertices labeled the next

letter of the alphabet. Edges are added by supplying the vertices in the text fields labeled Vertex

$l$ and Vertex $2$ and then clicking the Add Edge button. If the user enters a nonexistent vertex

name, an error message should be displayed in the text field at the bottom.

The four buttons at the bottom should analyze the graph. The Is Connected button should

indicate whether the graph is connected. The Has Cycles button should indicate whether the

graph has cycles. In both cases, an appropriate message should be displayed in the text field at

the bottom. The Depth First Search and the Breadth First Search buttons should display the list

of the vertices resulting from the corresponding search, starting at vertex A$.$

The program should consist of four classes. The first class should be an immutable class that

defines a vertex of the graph and contains the $x$ and $y$ coordinates of the vertex along with its

name. It should have a constructor and three getter methods.

The second class should be a class that defines the graph. You may use any graph representation

that allows an unlimited number of vertices and edges. It should have the following public

methods

A method to add a vertex

A method to add an edge

A method that checks whether the graph has cycles

A method to check whether the graph is connected

A method that retums a list of vertices resulting from a depth$-$first graph search

A method that returns a list of vertices resulting from a breadth$-$first graph search

You may add any other methods as needed.

The third class is should be an extension of the javafx Pane class that visually displays the

graph. It should contain an event handler that responds to mouse clicks that creates new vertices

and a method that is called to draw edges.

The fourth class should contain the main method and should create the GUI including all the

buttons and text fields. It should include event handlers for each of the buttons.