I have a simple, undirected graph for which $\;|E|=2|V|+5\;$ and in which every vertex has degree at least $\;5\;$. I'm asked what's the maximal number for $\;V\;$.
Now, this is how I thought: no loops or parallel edges allowed, which means that if the graph has one vertex then it automatically has to have other five, so $\;|E|\ge 6\;$ . But if I add one vertex more then I can connect it with other five of the first six vertices...It really is confusing.
And I read that there can also be non-connected simple graphs, though I'm not sure whether this applies to my case.
Any help will be appreciated.