A331236 Total cutting number of all simple connected graphs of order n.

0, 0, 1, 7, 43, 302, 2622, 31129, 564452, 17585400, 1006927107, 107458067322

Offset

1,4

Links

Table of n, a(n) for n=1..12.

F. Harary and P. A. Ostrand, How cutting is a cut point?, pp. 147-150 of R. K. Guy et al., editors, Combinatorial Structures and Their Applications (Proceedings Calgary Conference Jun 1969}), Gordon and Breach, NY, 1970. [Annotated scan of page 147 only.]

F. Harary and P. A. Ostrand, How cutting is a cut point?, pp. 147-150 of R. K. Guy et al., editors, Combinatorial Structures and Their Applications (Proceedings Calgary Conference Jun 1969}), Gordon and Breach, NY, 1970. [Annotated scan of pages 148, 149 only.]

Sean A. Irvine, Java program (github)

Simon Mukwembi and Senelani Dorothy Hove-Musekwa, On bounds for the cutting number of a graph, Indian J. Pure Appl. Math., 43 (2012), 637-649.

Formula

a(n) = Sum_{G} c(G) where the sum is over all graphs G with n vertices and c(G) is the cutting number of G.

a(n) = Sum_{k=0..(n-1)*(n-2)/2} A331422(n, k).

Crossrefs

Cf. A331237 (trees), A331422.

Sequence in context: A338675 A244938 A199483 * A042213 A193705 A164775

Adjacent sequences: A331233 A331234 A331235 * A331237 A331238 A331239

Keyword

nonn,more

Author

Sean A. Irvine, Jan 13 2020

Status

approved