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I'm looking for literature about multi/pseudo graphs and/or homomorphisms between them. Here by multi/pseudo graph (the terminology is not commonly agreed upon) I mean a graph that could have multiple edges between two vertices (which don't have to differ), also I would prefer literature that is not confined to finite cases. I've looked into the references given on the Wikipedia page on multigraphs, but just as I expected these cases are just mentioned shortly, as it happened in all graph books I've encountered yet.

My local university library doesn't list any books or other references given the key words "pseudo graph" or "multi graph", so I'm at loss here.

EDIT: The graph theory book of Bondy and Murty from 2008 suggested in the comments is a good start, as well as the graph theory book of Wilson from the 70's I've found in the mean time. But both of them only handle isomorphisms, not general homomorphisms. I still need literature about this.

SK19
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  • Is quiver the word you're looking for? – krirkrirk Feb 28 '18 at 12:26
  • @krirkrirk From the linked page I deduce that morphisms between quivers are always full homomorphisms between the multidigraphs, which is already a bit more restricted than I intended. However, I can't seem to find quiver related books in my university's library either, so it would be a start. – SK19 Feb 28 '18 at 12:39
  • I'm not sure this is what you're looking for but one can learn pretty much everything about quivers in this pdf – krirkrirk Feb 28 '18 at 12:57
  • @krirkrirk Thanks for the reference. Quivers seem to be an interesting point of view for graphs, but it isn't really what I'm looking for. I would like to look at abstract multigraphs without assigning vector spaces to them, even if it would be interesting. – SK19 Mar 01 '18 at 20:07
  • @MorganRodgers I know that they also use the terminology "graph". That's why it is so difficult to find literature about multigraphs by reading only the book titles. Going through all books is tiresome, I already started with that at my local math library. But it has the book of Bondy & Murty you referred to, so I will have a look at it today. – SK19 Mar 09 '18 at 11:46
  • @MorganRodgers The reference you gave is good and covers about 50% of the question. However Bondy & Murty don't seem to go into graph homomorphisms and only cover isomorphisms. I'm looking for some literature about homomorphisms between graphs, like http://www.mast.queensu.ca/~ctardif/articles/ghss.pdf where Hahn & Tardif only cover homomorphisms between simple graphs. If you would happen to know a good reference, together with the Bondy & Murty book you could write a satisfying answer :) – SK19 Mar 11 '18 at 13:13
  • What about this? link – Ripstein Mar 23 '18 at 10:52
  • @MrRipstein Looks very good! Mind to post this as an answer? – SK19 Mar 23 '18 at 22:50
  • Sure! Here it goes – Ripstein Mar 26 '18 at 07:08

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I recommend you this volume DIMACS workshop: Graphs, Morphisms, and Statistical Physics.

As the reference says: This volume is intended for graduate students and research mathematicians interested in probabilistic graph theory and its applications.Hope it suits your research on multi graphs and homomorphisms

Ripstein
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