A309805 -id:A309805 - cp's OEIS frontend

A371396 Maximum number of vertices of a chordal ring graph with diameter n.

6, 14, 20, 38, 48, 74, 88, 122, 140, 182, 204, 254, 280, 338, 368, 434, 468, 542, 580, 662, 704, 794, 840, 938, 988, 1094, 1148, 1262, 1320, 1442, 1504, 1634, 1700, 1838, 1908, 2054, 2128, 2282, 2360, 2522, 2604, 2774, 2860, 3038, 3120, 3314, 3408, 3602, 3700, 3902, 4004, 4214, 4320, 4538, 4648

Offset: 2

Miquel A. Fiol, Mar 21 2024

nonn

Given integers N (even) and c (odd) the chordal ring graph CR(N,c) is a bipartite graph with vertex set Z_N, and edges {i,i+1}, {i,i-1}, {i,i+c} if i is odd, and {i,i-c} if i is even.

If the conjecture below holds, then a(n) = 2*A309805(n) for n >= 3.

			For diameter n=3 the maximum number of vertices a(3)=14 is attained by the Heawood graph.

P. Morillo, F. Comellas, and M. A. Fiol, The optimization of chordal ring networks, Communication Technology, Eds. Q. Yasheng and W Xiuying, World Scientific,1987, pages 295--299.

B. W. Arden and H. Lee, Analysis of chordal ring networks, IEEE Trans. Comput. C-30 (1981), 291-295.
M. A. Reyes, C. Dalfó, and M. A. Fiol, Structural and Spectral Properties of Chordal Ring, Multi-ring and Mixed Graphs, arXiv:2409.00520 [math.CO2024], 2024 [See Table 6, p. 21]. Also in Symmetry 16 (2024), no. 9, 1135.
J. L. A. Yebra, M. A. Fiol, P. Morillo, and I. Alegre, The diameter of undirected graphs associated to plane tessellations, Ars Combin. 20-B (1985), 159-171.

Cf. A309805.

a(n) = (3*n^2+1)/2 if n is odd.

Conjecture: a(n) = (3/2)*n^2 - n if n is even and n > 2.

A079811 Sum of numbers read upward at a 45-degree angle in A079809.

Original entry on oeis.org

1, 2, 2, 6, 7, 10, 10, 18, 19, 24, 24, 36, 37, 44, 44, 60, 61, 70, 70, 90, 91, 102, 102, 126, 127, 140, 140, 168, 169, 184, 184, 216, 217, 234, 234, 270, 271, 290, 290, 330, 331, 352, 352, 396, 397, 420, 420, 468, 469, 494, 494, 546, 547, 574, 574, 630, 631

Offset: 1

Amarnath Murthy, Feb 10 2003

Index entries for linear recurrences with constant coefficients, signature (1,0,0,2,-2,0,0,-1,1).

Cf. A079808, A092542.

The two bisections are A309805 and twice A211538 (with leading zeros dropped).

Terms a(8) and beyond from Andrey Zabolotskiy, Jan 18 2024

cp's OEIS Frontend

A371396 Maximum number of vertices of a chordal ring graph with diameter n.

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