Question

What is the maximum number of edges present in a disconnected graph on
$n\ge 3vertices?$

• A. ${}^{(n-1)}{C}_2$
• B. ${(}^n{C}_2-1)$
• C. ${}^{(n-2)}{C}_2$
• D. $n-2$

Answer 1

The correct option is A ${}^{(n-1)}{C}_2$

Maximum number of edges in connected graph
${}^n{C}_2=\frac{n(n-1)}{2}$
So, by disconnected one vertex from it, we get :
$={}^{n-1}{C}_2=\frac{(n-1)(n-2)}{2}$
Ex : connected graph on 4 vertices :

Disconnected graph on 4 vertices :${=}^{(4-1)}{C}_2{=}^3{C}_2=3$