Connected graphs on n edges (A002905 ) vs Connected linegraphs (A003089)

Gordon Royle gordon at csse.uwa.edu.au
Thu Jun 5 07:50:05 CEST 2003


These two sequences differ only in one term... namely a(3) because there are
two graphs (K_3 and K_{1,3}) that have isomorphic linegraphs.

The numbers can be calculated by Polya enumeration, so I extended the
"linegraph" sequence from 16 terms to 24 terms; of course this has a
consequence for the "connected graphs by edges" sequence (which currently
has 19 terms).

It may be too much to ask to suggest that an extension to one should
automatically generate an extension to the other, but maybe it would be
possible to nominate that a sequence "depends" on another, in such a way
that a potential extender is automatically notified of other sequences that
should be updated sat the same time?

Too complicated?

Gordon







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