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Maximum number of simple graphs with no isolated vertices on n nodes with identical degree sequences.
0

%I #19 Aug 04 2019 05:15:15

%S 1,1,1,2,5,20,184,3020,65500

%N Maximum number of simple graphs with no isolated vertices on n nodes with identical degree sequences.

%H Peter Adams, Roger B. Eggleton, and James A. MacDougall, <a href="https://www.researchgate.net/publication/43500245">Taxonomy of Graphs of Order 10</a>, Congressus Numerantium, 180 (2006), 65.

%H Peter Adams, Roger B. Eggleton, and James A. MacDougall, <a href="https://people.smp.uq.edu.au/PeterAdams/research/poset10.html">Taxonomy of Graphs of Order 10</a>, Web page.

%o (Sage)

%o def max_graphs(n):

%o if n > 1:

%o count = defaultdict(int)

%o sequences = [tuple(graph.degree_sequence()) for graph in graphs(n) if graph and not 0 in graph.degree_sequence()]

%o for seq in sequences:

%o count[seq] += 1

%o max_cnt = max(count.values())

%o else:

%o return None

%o return max_cnt

%K nonn,hard,more

%O 2,4

%A _Sharat Chandra_, Jun 04 2019