A159847 - OEIS

A159847

The number of non-isomorphic n-node graphs with the maximal number of edges, and containing no three-cycles or four-cycles.

1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 3, 7, 1, 4, 1, 22, 14, 15, 1, 1, 3, 3, 7, 1, 6, 2, 1, 4, 1, 1, 2, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

The Moore graphs are unique examples of these graphs for their orders. Thus the fiftieth term in this sequence is 1.

Two additional values of this sequence determined: a(24)=1 and a(32)=1. [Michael Codish, Apr 09 2013]

REFERENCES

D. K. Garnick and N. A. Nieuwejaar, Non-isomorphic Extremal Graphs without Three-Cycles or Four-Cycles, Journal of Combinatorial Mathematics and Combinatorial Computing, 12(1992), 33-56.

LINKS

Table of n, a(n) for n=1..32.

J Backelin, Sizes of the extremal girth 5 graphs of orders from 40 to 49, arXiv preprint arXiv:1511.08128 [math.CO], 2015.

Michael Codish, Alice Miller, Patrick Prosser, and Peter J. Stuckey, Breaking Symmetries in Graph Representation, IJCAI 2013.

Alice Miller and Michael Codish, Graphs with girth at least 5 with orders between 20 and 32, arXiv:1708.06576 [math.CO], 2017.

CROSSREFS

Cf. A006856.

Sequence in context: A030338 A231148 A266649 * A327489 A257886 A144477

Adjacent sequences: A159844 A159845 A159846 * A159848 A159849 A159850

KEYWORD

nonn,hard,more

AUTHOR

David Garnick, Apr 23 2009

EXTENSIONS

a(22)-a(31) from Miller and Codish, David Garnick, Dec 24 2022

STATUS

approved