Let the maximum and minimum degress of a graph be denoted (as usual) by $\Delta$ and $\delta$ respectively.

A graph is almost regular if $\Delta-\delta=1$.

Now, here is a simple way to generate such graphs: start with a regular graph and delete a matching. Either that or add a matching.

An almost regular graph which is produced from a regular graph by the addition or removal of a mathing is obvious.

Can you find examples of non-obvious almost regular graphs? So far, I am unable to produce any but I have a feeling there ought to be some.

A follow-up question, in case non-obvious ones do exist, would of course be to estimate which case is more prevalent.

Let the maximum and minimum degress of a graph be denoted (as usual) by $\Delta$ and $\delta$ respectively.

A graph is almost regular if $\Delta-\delta=1$.

Now, here is a simple way to generate such graphs: start with a regular graph and delete a matching. Either that or add a matching.

An almost regular graph which is produced from a regular graph by the addition or removal of a matching is obvious.

Can you find examples of non-obvious almost regular graphs? So far, I am unable to produce any but I have a feeling there ought to be some.

A follow-up question, in case non-obvious ones do exist, would of course be to estimate which case is more prevalent.