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I'm working on a project in which we use a type of undirected graphs where loops (an edge from a vertex to itself) but NOT parallel edges (multiple edges with the same end vertices), and I was wondering if there exists a name for these types of graphs.

I noticed that in the case where parallel edges are allowed, some authors make the distinction between 'multigraphs' and 'pseudographs' to denote whether or not loops are permitted, but I have never seen such a distinction when multiple edges are not allowed.

If anyone has ever come across such a name, I would be gratefull, because it will probably look better than "Let G be a graph that is permitted to have loops".

user9934848
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1 Answers1

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A simple graph [1,2] is an unweighted, undirected graph containing no graph loops or multiple edges.

So you could either use that definition making it explicit the loops are allowed:

Let G be an unweighted, undirected graph containing loops but no multiple edges.

or could loosen the conditions of a simple graph:

Let G be a graph that is simple but may, additionally, contain looping edges.
MT0
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