Consider a simple connected graph $G$ with $n$ vertices and $n$ edges $(n > 2)$. Then, which of the following statements are true?
I think 'c' won't be ans because there will be exactly one cycle (as the graph is connected) not atleast. So only option 'd' is correct.
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
please comment on this:
No, C is not true as the graph will have exactly 1 cycle.