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A159847 The number of non-isomorphic n-node graphs with the maximal number of edges, and containing no three-cycles or four-cycles. 2
1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 3, 7, 1, 4, 1, 22, 14, 15, 1, 1, 3 (list; graph; refs; listen; history; text; internal format)



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]


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.


Table of n, a(n) for n=1..21.

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, 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.


Cf. A006856.

Sequence in context: A030338 A231148 A266649 * A327489 A257886 A144477

Adjacent sequences:  A159844 A159845 A159846 * A159848 A159849 A159850




David Garnick (dgarnick(AT)gmail.com), Apr 23 2009



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Last modified December 15 11:43 EST 2019. Contains 329999 sequences. (Running on oeis4.)