simple graph

Question

a)if a simple graph with n vertices is necessarily connected the minimum and maximum number of edges is (n-1) and nC2

am i right?

b)is a simple graph is always a connected graph? if not then y?

Comments

see this: http://mathworld.wolfram.com/SimpleGraph.html

Here you can see many graphs (which are simple) but not connected

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there are just 3 vertices with no edges...is it a simple graph?

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Yes. When I googled simple graph I found this:

A simple graph, also called a strictgraph (Tutte 1998, p. 2), is an unweighted, undirected graphcontaining no graph loops or multiple edges (Gibbons 1985, p. 2; West 2000, p. 2; Bronshtein and Semendyayev 2004, p. 346). A simple graph may be either connected or disconnected.

Answer 1

if a simple graph with n vertices is necessarily connected the minimum and maximum number of 

Minimum number of edges = connect n-1 vertices completely and then add one more edge.
= ((n-1)(n-2)/2) +1

Maximum edges  = make a complete grapth with n vertices = n(n-1)/2 = nC2

Comments

Minimum number of edges = connect n-1 vertices completely and then add one more edge. 
= ((n-1)(n-2)/2) +1

Didnt get this one? 

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@Arjun Sir I am not getting this. Min number of edges to make the graph connected necessarily should be n-1. Then why here n-1C2 + 1? This should be in case of sufficient number of edges not in case if necessary.

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If graph is Connected Graph, then min no. of edges is n-1. Converse is not true ( Take n = 4 and take edges as triangle)

But for saying graph is surely connected, we need atleast n-1C2 + 1 edges( Take Kn-1 and 1 vertex, and add edges between these 2 components)

Max no.of edges = nC2 in both cases as max will come only when graph is connected.