login
A355067
a(n) is the failed skew zero forcing number of P^3_n.
1
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
3,3
COMMENTS
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.
LINKS
T. Ansill, B. Jacob, J. Penzellna, and D. Saavedra, Failed skew zero forcing on a graph, Linear Algebra and its Applications, vol. 509 (2016), 40-63.
FORMULA
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
CROSSREFS
Sequence in context: A369218 A097356 A083522 * A108942 A025561 A342169
KEYWORD
nonn,easy
AUTHOR
STATUS
approved