Darren Narayan - cp's OEIS frontend

User: Darren Narayan

Darren Narayan has authored 2 sequences.

A355067 a(n) is the failed skew zero forcing number of P^3_n.

0, 1, 3, 3, 4, 4, 6, 5, 6, 7, 9, 8, 9, 10, 12, 11, 12, 13, 15, 14, 15, 16, 18, 17, 18, 19, 21, 20, 21, 22, 24, 23, 24, 25, 27, 26, 27, 28, 30, 29, 30, 31, 33, 32, 33, 34, 36, 35, 36, 37, 39, 38, 39, 40, 42, 41, 42, 43

Offset: 3

Aidan Johnson, Darren Narayan, and Andrew E. Vick, Jul 14 2022

P^3_n is the cube of path graph P_n.

Given a graph G where each vertex is initially considered filled or unfilled, we apply the skew color change rule, which states that a vertex v becomes filled if and only if it is the unique empty neighbor of some other vertex in the graph. The failed skew zero forcing number of G, is the maximum cardinality of any subset S of vertices on which repeated application of the skew color change rule will not result in all vertices being filled.

Georg Fischer, Table of n, a(n) for n = 3..1000
Thomas Ansill, Bonnie Jacob, Jaime Penzellna, and Daniel Saavedra, Failed skew zero forcing on a graph, Linear Algebra and its Applications (2016) Vol. 509, 40-63.
Aidan Johnson, Andrew Vick, Rigoberto Flórez, and Darren A. Narayan, Failed Skew Zero Forcing Numbers of Path Powers and Circulant Graphs, AppliedMath (2025) Vol. 5, No. 2, 32.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

CoefficientList[Series[x^3*(1 + 2*x + x^3 - x^4 - x^6 + x^8)/((1 - x)^2*(1 + x)*(1 + x^2)), {x, 0, 59}], x][[3 ;; -1]] (* Michael De Vlieger, Mar 28 2025 *)

a(n) = 3*floor((n-1)/4) + cos((n*Pi)/2) for n > 7.

G.f.: x^3*(1 + 2*x + x^3 - x^4 - x^6 + x^8)/((1 - x)^2*(1 + x)*(1 + x^2)). - Stefano Spezia, Jul 15 2022

A355399 a(n) is the failed skew zero forcing number of C^2_n.

Original entry on oeis.org

0, 1, 2, 4, 3, 4, 6, 5, 6, 8, 6, 8, 10, 8, 10, 12, 10, 12, 14, 12, 14, 16, 14, 16, 18, 16, 18, 20, 18, 20, 22, 20, 22, 24, 22, 24, 26, 24, 26, 28, 26, 28, 30, 28, 30, 32, 30, 32, 34, 32, 34, 36, 34, 36, 38, 36, 38, 40, 38, 40, 42, 40, 42, 44, 42, 44, 46, 44, 46

Offset: 3

Darren Narayan, Andrew E. Vick, and Aidan Johnson, Jun 30 2022

Given a graph G where each vertex is initially considered filled or unfilled, we apply the skew color change rule, which states that a vertex v becomes filled if and only if it is the unique empty neighbor of some other vertex in the graph. The failed skew zero forcing number of G, is the maximum cardinality of any subset S of vertices on which repeated application of the color change rule will not result in all vertices being filled. Note that C^2_n = Ci_n(1,2) is the square of C_n.

Thomas Ansill, Bonnie Jacob, Jaime Penzellna, and Daniel Saavedra, Failed skew zero forcing on a graph, Linear Algebra and its Applications, vol. 509 (2016), 40-63.
Aidan Johnson, Andrew Vick, Rigoberto Flórez, and Darren A. Narayan, Failed Skew Zero Forcing Numbers of Path Powers and Circulant Graphs, AppliedMath (2025) Vol. 5, No. 2, 32.
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Cf. A008611, A343648.

a(n) = 2*floor(n/3) + 2*(ceiling(n/(3*floor(n/3) + 1)) - floor(n/(3*floor(n/3) +1 )) - 1) for n >= 11.

a(n) = 2*A008611(n-3) for n >= 11.

More terms from Stefano Spezia, Jun 30 2022

cp's OEIS Frontend

User: Darren Narayan

A355067 a(n) is the failed skew zero forcing number of P^3_n.

Views

Author

Keywords

Comments

Links

Programs

Mathematica

Formula