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Maximum number of vertices of a chordal ring mixed graph CRM(N,c) with diameter n.
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%I #17 Aug 02 2024 19:16:33

%S 8,10,18,16,32,34,50,44,72,74,98,88,128,130,162,148,200,202,242,224,

%T 288,290,338,316,392,394,450,424,512,514,578,548,648,650,722,688,800,

%U 802,882,844,968,970,1058,1016,1152,1154

%N Maximum number of vertices of a chordal ring mixed graph CRM(N,c) with diameter n.

%H C. Dalfó, G. Erskine, G. Exoo, M. A. Fiol, and J. Tuite, <a href="https://doi.org/10.48550/arXiv.2403.18943">On bipartite (1, 1, k)-mixed graphs</a>, (2024).

%F If n is odd, a(n) = (n+1)^2/2.

%F Conjecture: If n is even, n=0 mod 4, a(n) = n^2/2+2;

%F If n (> 2) is even, n=2 mod 4, a(n) = n*(n/2 - 1) + 4.

%F Conjectured g.f.: 2*(1 + x + 2*x^2 + x^3 + 2*x^4 - 3*x^5 + 4*x^6 - x^7 + x^8)/((1 - x)^3*(1 + x + x^2 + x^3)^2). - _Stefano Spezia_, Jul 14 2024

%e For n = 9, the maximum number of vertices a(9) = 50 is attained by the chordal ring mixed graph CRM(50,9).

%Y Cf. A371396.

%K nonn

%O 3,1

%A _Miquel A. Fiol_, Jul 14 2024