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.

  • $\begingroup$ Is quiver the word you're looking for? $\endgroup$ – krirkrirk Feb 28 '18 at 12:26
  • $\begingroup$ @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. $\endgroup$ – SK19 Feb 28 '18 at 12:39
  • $\begingroup$ I'm not sure this is what you're looking for but one can learn pretty much everything about quivers in this pdf $\endgroup$ – krirkrirk Feb 28 '18 at 12:57
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    $\begingroup$ These are often just called "graphs" (if you disallow multiple edges and loops then they are simple graphs). There is lots & lots & lots of literature out there, are you looking for something specific? $\endgroup$ – Morgan Rodgers Mar 9 '18 at 6:28
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    $\begingroup$ Bondy & Murty prove a lot about graphs without assuming they are simple or finite. $\endgroup$ – Morgan Rodgers Mar 9 '18 at 6:30

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


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