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The maximum number of facets among all symmetric edge polytopes for connected graphs on n vertices having m edges for n >= 2 and m between n-1 and binomial(n,2).
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%I #24 Mar 04 2023 22:32:15

%S 2,4,6,8,12,12,14,16,30,36,28,28,28,30,32,60,72,72,84,68,68,60,60,60,

%T 62,64,140,180,216,168,168,196,180,148,148,132,132,124,124,124,126,

%U 128,280,360,432,432,504,408,408,392,420,360,372,324,308,276,276,260,260,252,252,252,254

%N The maximum number of facets among all symmetric edge polytopes for connected graphs on n vertices having m edges for n >= 2 and m between n-1 and binomial(n,2).

%H B. Braun and K. Bruegge, <a href="https://arxiv.org/abs/2201.13303">Facets of Symmetric Edge Polytopes for Graphs with Few Vertices</a>, arXiv:2201.13303 [math.CO], 2022.

%e The triangular array starts:

%e [2]: 2;

%e [3]: 4, 6;

%e [4]: 8, 12, 12, 14;

%e [5]: 16, 30, 36, 28, 28, 28, 30;

%e [6]: 32, 60, 72, 72, 84, 68, 68, 60, 60, 60, 62;

%e [7]: 64, 140, 180, 216, 168, 168, 196, 180, 148, 148, 132, 132, 124, 124, 124, 126

%Y Cf. A360409, A000079.

%K nonn,tabf

%O 2,1

%A _Benjamin Braun_, Feb 06 2023