3) (25 pnt.) Solve the following questions a) Draw the rooted tree which is given with...

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3) (25 pnt.) Solve the following questions a) Draw the rooted tree which is given with prefix form of (x +B-DF + AC). b) Draw the rooted tree which is given with postfix form of (ED-A + BC-FX+). 4) (25 pnt.) The simple graph K is given as 4 i) Find a Hamiltonian cycle on K. ii) Find the Euclidian cycle for graph K, if there exists any. Also, state the reason for your answer. iii) Find the diameter of K. Hint: The diameter is the maximum of all shortest path between pairs of vertices iv) By stating the reason, use smallest possible number of colors for coloring the graph K. 3) (25 pnt.) Solve the following questions a) Draw the rooted tree which is given with prefix form of (x +B-DF + AC). b) Draw the rooted tree which is given with postfix form of (ED-A + BC-FX+). 4) (25 pnt.) The simple graph K is given as 4 i) Find a Hamiltonian cycle on K. ii) Find the Euclidian cycle for graph K, if there exists any. Also, state the reason for your answer. iii) Find the diameter of K. Hint: The diameter is the maximum of all shortest path between pairs of vertices iv) By stating the reason, use smallest possible number of colors for coloring the graph K.