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A355399
a(n) is the failed skew zero forcing number of C^2_n.
0
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
3,3
COMMENTS
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.
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) = 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.
CROSSREFS
Sequence in context: A369430 A360691 A302707 * A224714 A089169 A291563
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Stefano Spezia, Jun 30 2022
STATUS
approved