University maths question

I have been asked to complete the following question without being taught about the topic.

Create a graph which has:
• 5 vertices;
• at least one odd vertex;
• a vertex-magic labelling† with magic constant 8.

My first instinct is to draw a pentagon and go through trial and error, but obviously I don't know how many edges each vertex will have. I am aware that the magic constant means that I need labelling of the edges such that the sum of labels at each vertex is 8. Please correct me if I am wrong.
How do I go about this problem?

Can't say I'm familiar with this, but from a bit of googling, I doubt it's feasible.

But the first thing to be clear about is what is meant by "vertex-magic labelling" in this question, as your usage doesn't seem to conform to what's generally available on Google. Do you have a definition?

The definition given in the question is:
A labelling of the edges such that the sum of labels at each vertex is a constant

OK, this doesn't look to be the usual definition of vertex-magic labelling.

If we make the usual restriction, that the labelling is a bijection between the set of edges and the set {1,2,3,...,k}, for some k to be determined.

Then by considering the sum over all the vertices we can show that no such labelling can exist.

But this seems contrary to the way the question is posed, as it makes no use of "at least one odd vertex".

So, what are our labels allowed to be? And must they be unique?

Might help to know some background to the question: Where is it from? What have you covered recently in graph theory? Etc. as appropriate.

The part of the module is called graph theory and topology. We have just covered Hamiltonian and eulerian graphs, then went onto magic squares