Use the graph provided below for the following questions. Please, follow the questions and requirements strictly.

1)A) For graph 1, list the vertices of a depth-first search starting at vertex A. Choose the alphabetically lower vertex when you have a choice.

b) For graph 1, list the vertices of a breadth-first search starting at vertex A. Choose the alphabetically lower vertex when you have a choice.

c) Determine if graph 2 has an Euler circuit, an Euler path but not an Euler circuit, or neither, If the graph has a circuit or path, list the vertices in the circuit or path. If a circuit or path does not exist, give a brief explanation why it doesn't exist.

d) Determine if graph 3 has an Euler circuit, an Euler path but not an Euler circuit, or neither. If the graph has a circuit or path, list the vertices in the circuit or path. If a circuit or path doesn't exist, give a brief explanation why it doesn't exist.

e) Determine if graph 2 has a Hamilton Circuit, A Hamilton path but not a Hamilton circuit, or neither. If the graph has a circuit or path, list the vertices in the circuit or path. If a circuit or path doesn't exist, give a brief explanation why it doesn't exist.

f) Determine if graph 3 has a Hamilton circuit, a Hamilton path but not a Hamilton circuit, or neither . if the graph has a circuit or path, list the vertices in the circuit or path. If a circuit or path doesn't exist, give a brief explanation why it doesn't exist.

g) Determine the chromatic number for graph 2. provide a coloring for the graph. for each color, provide a list of vertices that have been assigned that color.

h) Using graph 4, list the shorted path from vertex A to each of the other vertices in the graph.

Graph 1 Graph 2 Graph 3 2 5 7 1 2 2 3 7 3 Graph 4