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A288027 Number of minimal edge covers in the grid graph P_n X P_n. 3
0, 2, 38, 1834, 419710, 356269056, 1163645044100, 15000387107144576, 749707067231291403016 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
A minimal edge cover is an edge cover such that the removal of any edge in the cover destroys the covering property. Equivalently, these are the edge covers whose connected components are stars.
LINKS
Eric Weisstein's World of Mathematics, Grid Graph
Eric Weisstein's World of Mathematics, Minimal Edge Cover
EXAMPLE
In the 3 X 3 grid, the minimal edge covers up to rotation and reflection are:
.__.__. .__.__. .__.__. .__.__. .__.__. .__. .
.__.__. . . . .__. . . .__. . | . . | |
.__.__. | | | .__. | |__. | | .__| | .__.
The first two of these need to be counted 2 and 4 times and the rest which have no symmetry 8 times so a(3) = 38.
CROSSREFS
Main diagonal of A288025.
Cf. A286913.
Sequence in context: A187544 A187545 A246484 * A184994 A334554 A348162
KEYWORD
nonn,more
AUTHOR
Andrew Howroyd, Jun 04 2017
EXTENSIONS
a(1) corrected by Andrew Howroyd, Jan 29 2023
STATUS
approved

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Last modified March 28 04:05 EDT 2024. Contains 371235 sequences. (Running on oeis4.)