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A374622
Maximum number of vertices of a chordal ring mixed graph CRM(N,c) with diameter n.
0
8, 10, 18, 16, 32, 34, 50, 44, 72, 74, 98, 88, 128, 130, 162, 148, 200, 202, 242, 224, 288, 290, 338, 316, 392, 394, 450, 424, 512, 514, 578, 548, 648, 650, 722, 688, 800, 802, 882, 844, 968, 970, 1058, 1016, 1152, 1154
OFFSET
3,1
LINKS
C. Dalfó, G. Erskine, G. Exoo, M. A. Fiol, and J. Tuite, On bipartite (1, 1, k)-mixed graphs, (2024).
FORMULA
If n is odd, a(n) = (n+1)^2/2.
Conjecture: If n is even, n=0 mod 4, a(n) = n^2/2+2;
If n (> 2) is even, n=2 mod 4, a(n) = n*(n/2 - 1) + 4.
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
EXAMPLE
For n = 9, the maximum number of vertices a(9) = 50 is attained by the chordal ring mixed graph CRM(50,9).
CROSSREFS
Cf. A371396.
Sequence in context: A121846 A059094 A302166 * A287270 A299988 A143617
KEYWORD
nonn
AUTHOR
Miquel A. Fiol, Jul 14 2024
STATUS
approved