K - regular bipartite graph means we will have bipartite graph of the form K2,2 , K3,3 etc..
In general in Kk,k the degree of each vertex will be k and it will be a bipartite graph..
Now coming to the cut edge , it means that removal of such edge will disconnect the entire edge..
But we do not get any such edge in K - regular bipartite graph , provided K >= 2 , because after removal of that edge , then the degree of the vertex on which it was incident will decrease by 1 only ..But being K >= 2 , the minimum degree that the vertex may have is 1 after removal of an edge from this graph..Thus ensuring the connectivity of the graph.
.Had K >= 1 then there would have been a possibility of degree of that particular vertex = 0 and in that case that vertex would be isolated from the remaining graph and in other words the original graph would get disconnected..
I hope this reasoning helps you..
Thus no edge will not disconnect the K regular bipartite graph on its removal.So no existence of cut edge for such graph..