I need to give a talk about Hopf algebras and I would like to give a (at least) 5 minutes introduction using Feynman diagrams as a motivation. I'm looking for a not-so-heavy reference explaining how the notions of product and coproduct arises from Feynman diagrams.
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Have you had a look at the book by Connes and Marcolli "Noncommutative Geometry, Quantum Fields and Motives" (its available online 1)?
The book first introduces Feynman diagrams and rules and then goes on to cast it in Hopf algebraic language. I think I recall seeing some computations along the line of your question in there.
I guess this answer is way too late to be useful to the OP, but there's of course also the book "Knots and Feynman Diagrams" by Dirk Kreimer.
I also guess my answer is too late to be useful to the OP. I think it is not an easy work to explain how the notions of product and coproduct arises from Feynman diagrams. Because I think you need much time (more than 5 minutes) to explain what is the Feynman diagram firstly. Why not use another combinatorical object---rooted trees? Just one minutes， all the audiences can know it. Maybe you can use Connes-Kreimor Hopf algebras to explain what you want. What more， for the coproduct of Connes-Kreimor Hopf algebras， there is an interesting combinatorics description. If you like， I suggest you to look Foissy's paper http://loic.foissy.free.fr/pageperso/p11.pdf
