# Difference between graph and multigraph

Does there exist a multigraph $$G$$ of order $$8$$ such that the minimal $$d(G) = 0$$ while maximal $$d(G) = 7$$? What if ‘multigraph $$G$$’ is replaced by ‘graph $$G$$’?

Answer: such multigraph does not exist, but graph?

• Since this is your second question on the matter, allow me to tell you a tiny tip: you will notice that as you type in tags for this question, there should be a short description on when you should use the tag. If you will read it, you'll then notice that it is graph-theory and not graph that you should be using as the tag. I will retag this for you for now, but please be more attentive the next time. – J. M. is a poor mathematician Jul 27 '12 at 13:47
• alright! thank you. I was writing graph theory with a space and not with a '-' – Intellectual_ Jul 27 '12 at 14:01
• I'm not clear as to why a multigraph with these properties does not exist. As you can have multiple edges between a pair of vertices, pick two, put seven edges between them and add no other edges. Then the other 6 vertices have degree 0. – Luke Mathieson Jul 27 '12 at 14:24
• Isn't every graph trivially a multigraph? – JeffE Jul 27 '12 at 15:49