1. ## graph help

how many subgraphs with at least one vertex does k₃ (complete graph with 3 vertices) have? show why

A simple graph is an undirected graph that has no loops and no more than one edge between any two vertices. If the simple graph G has v vertices and e edges how many edges does the complement G¯ have ?

Draw all nonisomorphic simple graph with five vertices and three edges?

Show that if G is a directed graph, then it is possible to remove vertices to disconnect G if and only if G is not a complete graph.

2. ## Re: graph help

Originally Posted by Bedejay
how many subgraphs with at least one vertex does k₃ (complete graph with 3 vertices) have? show why

A simple graph is an undirected graph that has no loops and no more than one edge between any two vertices. If the simple graph G has v vertices and e edges how many edges does the complement G¯ have ?

Draw all nonisomorphic simple graph with five vertices and three edges?

Show that if G is a directed graph, then it is possible to remove vertices to disconnect G if and only if G is not a complete graph.
You have posted a list of questions. You have shown absolutely no effort.
This is not a homework service.

A triangle is $K_3$, so you post the answer to the first.

If graph $\mathcal{G}$ has $N$ vertices and $E$ edges then $\overline{\mathcal{G}}$ has $N$ vertices and $\binom{N}{2}-E$ edges. WHY?

Now you do some work!