If you have doubt regarding tree edge, back edge , cross edge then you can see Here
Some good questions like this are--
Back Edge : an edge that connects a vertex to a vertex that is it's ancestor.
Start the $BFS$ from vertex $A$ then you take : $AB,AC,AD$, they are tree edges.
Now you take $BC$ it is a cross edge, then $CD$ it is also a cross edge then $DE$ this is a tree edge.
Then you can take $EB$ this is a cross edge.
So, there are no back edges but still a cycle $EBCD$ exists.
@Sandy Sharma by mistake i gave you a wrong example, now i have corrected it. If it answer all your queries and is correct you can select it as the answer.
@Shobhit Joshi plz explain back edge and cross edge definitions...I don't know anything about it
Back edge : Edge $(u,v)$ in the tree traversal in which $v$ is the ancestor of $u$
Forward edge : Edge $(u,v)$ in the tree traversal in which $v$ is one of the descendants of $u$
Cross edge : Edge $(u,v)$ in the tree traversal in which $v$ is neither the ancestor not the descendant of $u$
wiki link : here
@Shobhit Joshi how EB is cross edge in your original answer?
Watch video of this comment it will clear all your doubts--https://gateoverflow.in/235758/breadth-first-search?show=284709#c284709
Thanks @Verma Ashish brother!
@Shobhit Joshi As you said
After taking AB,AC,ADAB,AC,AD, they as tree edges.
How can we take take BC , as C will already be visited node.
@Sandy Sharma that's why i said it is a cross edge not a tree edge