Consider a simple connected graph $G$ with $n$ vertices and $n$ edges $(n > 2)$. Then, which of the following statements are true?
This seems like multiple answer questions.
Here we have $n$ vertices & $n$ edges. So we must have cycle.
So (C) has at least one cycle is True & (A) is false.
(D) The graph obtained by removing any two edges from $G$ is not connected $\rightarrow$ This is true, for graph of $n$ vertices to be connected, we need at least $n-1$ edges. If we remove $2$ out of $n$, we get $n-2$ edges, which can connect at max $n-1$ vertices. $1$ Vertex at least will be disconnected. So D is true.
(B) is false as if graph is cyclic graph then removing any edge will not disconnect graph.
Answer $\rightarrow$ (C) & (D).
hence c and d
Option (C) might not be correct because they have used the word "at least one cycle" while a graph with n vertices and n edges, graph will contain exactly 1 cycle.
But 'at least' contains the possibility of 'exactly one', hence option (C) also can be considered as true statement.
completely agree with @ Manu thakur here "Attest " won't be right it had "exactly one" then it would have been also the option so only "d" right here
No, C is not true as the graph will have exactly 1 cycle.
yes sir TRUE... working on it :). But this...