A343213 -id:A343213 - cp's OEIS frontend

A343209 Number of spanning trees of the graph of the n-th Johnson solid.

45, 121, 1815, 24000, 297025, 78250050, 361, 3509, 30976, 27216, 403202, 75, 1805, 1728, 31500, 508805, 207368, 1609152, 227402340, 29821320745, 8223103375490, 37158912, 15482880000, 5996600870820, 1702422879696000, 1176, 324900, 29859840, 30950832, 2518646460

Offset: 1

Pontus von Brömssen, Apr 08 2021

Terms are taken from the paper by Horiyama and Shoji, verified by Pontus von Brömssen.

			The gyrobifastigium (J26) has a(26) = 1176 spanning trees.

Pontus von Brömssen, Table of n, a(n) for n = 1..92
Takashi Horiyama and Wataru Shoji, The number of different unfoldings of polyhedra, The 29th European Workshop on Computational Geometry, Technische Universität Braunschweig 2013, 143-146. [Apparently, two pairs of Johnson solids have switched numbers in Table 2, namely J32 <-> J33 and J40 <-> J41.]
Wikipedia, List of Johnson solids

Cf. A242731, A343210, A343213.

A343432 Sorted numbers of spanning trees in the graphs of the Archimedean solids.

Original entry on oeis.org

6000, 331776, 32400000, 101154816, 301056000000, 89904012853248, 208971104256000, 12418325780889600, 4982259375000000000, 375291866372898816000, 201550864919150779950956544000, 438201295386966498858139607040000000, 21789262703685125511464767107171876864000

Offset: 1

Pontus von Brömssen, Apr 15 2021

The duals (Catalan solids) have the same number of spanning trees as their Archimedean counterparts.

			The solids are in order:
  truncated tetrahedron (6000),
  cuboctahedron (331776),
  truncated cube (32400000),
  truncated octahedron (101154816),
  rhombicuboctahedron (301056000000),
  snub cube (89904012853248),
  icosidodecahedron (208971104256000),
  truncated cuboctahedron (12418325780889600),
  truncated dodecahedron (4982259375000000000),
  truncated icosahedron (375291866372898816000),
  rhombicosidodecahedron (201550864919150779950956544000),
  snub dodecahedron (438201295386966498858139607040000000),
  truncated icosidodecahedron (21789262703685125511464767107171876864000).

Cf. A343209, A343213, A343433.

A358960 Number of directed Hamiltonian paths of the Platonic graphs (in the order of tetrahedral, cubical, octahedral, dodecahedral, and icosahedral graph).

Original entry on oeis.org

24, 144, 240, 3240, 75840

Offset: 1

Seiichi Manyama, Dec 07 2022

a(n)/2 is the number of undirected Hamiltonian paths of the Platonic graph corresponding to a(n).

From symmetry, a(n) is a multiple of A063723(n).

Seiichi Manyama, Python program (github)
Eric Weisstein's World of Mathematics, Tetrahedral Graph
Eric Weisstein's World of Mathematics, Cubical Graph
Eric Weisstein's World of Mathematics, Octahedral Graph
Eric Weisstein's World of Mathematics, Dodecahedral Graph
Eric Weisstein's World of Mathematics, Icosahedral Graph

Cf. A053016, A063723, A268283, A343213.

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A343209 Number of spanning trees of the graph of the n-th Johnson solid.

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A343432 Sorted numbers of spanning trees in the graphs of the Archimedean solids.

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A358960 Number of directed Hamiltonian paths of the Platonic graphs (in the order of tetrahedral, cubical, octahedral, dodecahedral, and icosahedral graph).

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