[Nauty] Connected multigraphs with multiloops with degree <= 4

Daniele Degiorgi degiorgi at hispeed.ch
Thu Mar 3 15:49:52 AEDT 2022

It seems to me that in a connected multigraph a node with more than one loop
has degree >= 4 and exactly 4 only if it is the only node in the graph.
Thus, in my opinion, graphs with more than one node can only contains simple

Hope this can help.


-----Original Message-----
From: Nauty <nauty-bounces at anu.edu.au> On Behalf Of Sean A. Irvine
Sent: giovedì, 3 marzo 2022 03:30
To: nauty at anu.edu.au
Subject: [Nauty] Connected multigraphs with multiloops with degree <= 4


I am interested in generating all connected multigraphs with maximum degree
4 (including graphs with multiloops). I thought I would be able to do this
using multig, but I cannot get the loops to work in the way that I want.
The help seems to suggest multig can only handle loops for regular graphs,
but I need all combinations of loops up to degree 4.  Any advice?

This is for an attempt to reproduce and extend a sequence in the OEIS:


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