login
Number of unlabeled graphs with n edges, no nodes of degree 1 and no cut nodes, under "series-equivalence"; multiple edges are allowed.
3

%I #5 Mar 30 2012 16:48:56

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

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

%C 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-.

%C 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.

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

%Y Cf. A058642.

%K nonn,nice,more

%O 1,3

%A _N. J. A. Sloane_, Dec 30 2000