A374622 Maximum number of vertices of a chordal ring mixed graph CRM(N,c) with diameter n.

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

Table of n, a(n) for n=3..48.

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

Adjacent sequences: A374619 A374620 A374621 * A374623 A374624 A374625

Keyword

nonn

Author

Miquel A. Fiol, Jul 14 2024

Status

approved