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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

%I #35 Jan 01 2023 09:43:04

%S 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

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

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

%C Two additional values of this sequence determined: a(24)=1 and a(32)=1. [_Michael Codish_, Apr 09 2013]

%D 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.

%H J Backelin, <a href="http://arxiv.org/abs/1511.08128">Sizes of the extremal girth 5 graphs of orders from 40 to 49</a>, arXiv preprint arXiv:1511.08128 [math.CO], 2015.

%H Michael Codish, Alice Miller, Patrick Prosser, and Peter J. Stuckey, <a href="http://www.cs.bgu.ac.il/~mcodish/Papers/Pages/ijcai2013.html">Breaking Symmetries in Graph Representation</a>, IJCAI 2013.

%H Alice Miller and Michael Codish, <a href="https://arxiv.org/abs/1708.06576">Graphs with girth at least 5 with orders between 20 and 32</a>, arXiv:1708.06576 [math.CO], 2017.

%Y Cf. A006856.

%K nonn,hard,more

%O 1,4

%A _David Garnick_, Apr 23 2009

%E a(22)-a(31) from Miller and Codish, _David Garnick_, Dec 24 2022

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