Finally, the plotting function should be modified toĪllgraphsplot := Graph, PlotLabel -> Last, To have the correct symmetry factors, we should also modify Apply to Apply!]. So as to consider permutations of internal vertices only. If the user wishes to label the 1-valent vertices (an operation that is useful in physics), they shall modify the code as follows: in permutations, change The graphs considered herein are unlabelled. If we do so, the second example above becomes Such graphs can be eliminated by setting Δ:=0 at the beginning of the code. Idem for any other criterion.Īs the examples above show, the graphs contain self-loops (a.k.a. Alternatively, if the user wishes to obtain k-edge-connected graphs, they may modify the code to Select&] for some k. If the user wishes to obtain disconnected graphs too, they shall modify the code Select&] to just X. (The plot title is the symmetry factor of the corresponding graph.)įor efficiency, the function allgraphs generates connected graphs only. To plot these lists as actual graphs, we use allgraphsplot := Graph, PlotLabel -> Last] & allgraphs This function generates all graphs represented as lists. I'm using the words "Feynman diagrams" for indexing purposes, but the question is in fact purely graph-theoretic.
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