An undirected graph G is BIPARTITE if its vertices can be partitioned into two sets X and Y such that every edge in G has one end vertex in X and the other in Y$.$ Based on this definition we can conclude that an undirected graph G is bipartite if and only if

Question $14$Answer

a$.$

G does not have any cycle of length $3$ or more $($length of a cycle is the number of edges on it$)$

b$.$

in BFS$($G$)$ there is no edge between two vertices with the same BFS$-$depth

c$.$

in DFS$($G$)$ there is no edge between two vertices with the same DFS$-$depth

d$.$

G does not have any cycle of length $3$ or $5($length of a cycle is the number of edges on it$)$