$(5$ pts$)$ Given the graph, choose the INvalid path when the breadth$-$first search is used, and $E$ is the starting vertex.

a$)E,B,D,A,C$

b$)E,C,B,A,D$

c$)$ E$,$ B$,$ D$,$ C$,$ A

d$)E,D,B,A,C$

e$)$ E$,$ D$,$ B$,$ C$,$ A