A058668 Number of unlabeled graphs with n edges, no nodes of degree 1 and no cut nodes, under "series-equivalence"; multiple edges are allowed.

0, 1, 2, 5, 6, 13, 28

Offset: 1

Author

N. J. A. Sloane, Dec 30 2000

Keywords

• nonn
• nice
• more

Comments

Under "series-equivalence" two graphs are equivalent if one can be obtained from the other by exchanging two subgraphs in series: replacing -A-B- by -B-A-.

Start with the graph consisting of a single edge together with the graphs described in A058642; apply the operations of replacing edges by two edges in series or parallel; discard equivalent graphs; the result is A058668.

References

• B. D. H. Tellegen, Geometrical configurations and duality of electrical networks, Philips Technical Review, 5 (1940), 324-330.

Crossrefs

Cf. A058642.