# Graph Theory - Component

I was asked to check if there are a graph with the following condition?

(a) It has $$3$$ components, $$20$$ vertices and $$16$$ edges

(b) It has $$7$$ vertices, $$10$$ edges, and more than two components.

However I am really confused with the definition of component, the definition I have checked is

a connected component (or just component) of an undirected graph is a subgraph in which any two vertices are connected to each other by paths

And then when I am trying to find a graph in (a), its always easy to find more than $$3$$ subgraph in a big graph with $$20$$ vertices, so ill assume the answer is no. But how should I prove this or am I doing it completely wrong?

• Connected graph edges are at least the number of vertices minus one. The minimum of edges is achieved for trees. – Somos Feb 25 at 5:20
• Your definition of component is seriously wrong. What is your source for that definition? Did you quote it exactly word for word? – bof Feb 25 at 7:56

Say we have $$a,b,c$$ vertices in components, so $$a+b+c+=20$$. Then each component must have at least $$a-1$$, $$b-1$$ and $$c-1$$ edges, so we have at least $$a-1+b-1+c-1 = 17$$ edges. A contradiction.
It is possible, take $$K_5$$ and two isolated vertices.