If a graph has n vertices and n − 2 or fewer can it be connected? Why?

To check:

Whether a graph, having n vertices and n-2 or fewer edges, is connected or not.

Given information:

Graph with n​ vertices  and n−2 or fewer edges.

Concept used:

Any tree with n vertices has n−1 edges and total degree is 2(n−1).

Calculation:

Claim: such a graph cannot be connected.

Reason: if possible suppose that the graph is connected then the graph or any of its sub graph with all the vertices can be a tree because a graph and all of its sub graph with n vertices has edges fewer than n−1