A288027 Number of minimal edge covers in the grid graph P_n X P_n.

0, 2, 38, 1834, 419710, 356269056, 1163645044100, 15000387107144576, 749707067231291403016

Offset: 1

Author

Andrew Howroyd, Jun 04 2017

Keywords

• nonn
• more

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.

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Grid Graph
• Eric Weisstein's World of Mathematics, Minimal Edge Cover

Crossrefs

Main diagonal of A288025.

Cf. A286913.

Extensions

a(1) corrected by Andrew Howroyd, Jan 29 2023