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A052445 Number of simple exactly-4-connected unlabeled n-node graphs. 5
0, 0, 0, 1, 0, 3, 21, 345, 13429, 1109105, 162318088 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

This counts graphs whose connectivity is exactly 4. However, the numbers are not correct: the smallest 4-connected graph is the complete graph K_5, so the initial terms are incorrect. See A086216 and A259862 for more information. - N. J. A. Sloane, Jul 08 2015

This is the column k = 4 of A259862, but with a(4) = 1 instead of 0 and a(5) = 0 instead of 1. These deviations from A259862 arise from slightly non-conventional definition of k-connectivity: in this sequence, a graph is considered exactly-4-connected if we can remove 4 vertices and get a graph with the number of connected components other than 1, but cannot do that with removing just 3 vertices; this definition differs from the conventional one only when we consider K_4, which becomes exactly-4-connected, and K_5, which becomes not exactly-4-connected. The same can be said about A052442-A052444. - Andrey Zabolotskiy, Nov 20 2017

LINKS

Table of n, a(n) for n=1..11.

Brendan McKay, confusion over k-connected graphs, posting to Sequence Fans Mailing List, Jul 08 2015.

Eric Weisstein's World of Mathematics, k-connected Graph.

FORMULA

a(n) = A086216(n) - A086217(n) for n > 5. - Andrey Zabolotskiy, Nov 20 2017

EXAMPLE

The a(6) = 3 exactly-4-connected 6-node graphs are the complete graph K_6 with 1, 2, or 3 non-adjacent edges removed.

CROSSREFS

Cf. A052442, A052443, A052444, A086216, A086217, A259862.

Sequence in context: A113085 A240936 A083228 * A186271 A101389 A108716

Adjacent sequences:  A052442 A052443 A052444 * A052446 A052447 A052448

KEYWORD

nonn,more,hard

AUTHOR

Eric W. Weisstein

EXTENSIONS

Partially edited by N. J. A. Sloane, Jul 08 2015 at the suggestion of Brendan McKay

a(8)-a(11) copied from A259862 by Andrey Zabolotskiy, Nov 20 2017

STATUS

approved

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Last modified January 18 20:52 EST 2018. Contains 297865 sequences.