A331236 - OEIS

%I #14 Dec 19 2024 21:18:26

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

%N Total cutting number of all simple connected graphs of order n.

%H F. Harary and P. A. Ostrand, <a href="/A002887/a002887.pdf">How cutting is a cut point?</a>, 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.]

%H F. Harary and P. A. Ostrand, <a href="/A002887/a002887_1.pdf">How cutting is a cut point?</a>, 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.]

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a331/A331236.java">Java program</a> (github)

%H Simon Mukwembi and Senelani Dorothy Hove-Musekwa, <a href="https://doi.org/10.1007/s13226-012-0038-8">On bounds for the cutting number of a graph</a>, Indian J. Pure Appl. Math., 43 (2012), 637-649.

%F 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.

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

%Y Cf. A331237 (trees), A331422.

%K nonn,more

%O 1,4

%A _Sean A. Irvine_, Jan 13 2020