Enumerate graphs with hexagonal faces The Next CEO of Stack OverflowIntuition about the faces in the connected planar graphs“faces” of a non-planar graphDraw a cubic planar graph with six faces of degree $4$ and one with $6$…Genus and faces of a graphHow to find a planar graph if I know that it has 7 faces with certain sizes?Number of vertices in hexagonal tiling of rectangleAttempting to understand what a “Face” in planar graph to count faces correctlyplanar graphs and number of facesCount of maximal sextic toroidal graphsFiniteness of regular planar simple graphs with their faces bounded by cycles of the same length
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Enumerate graphs with hexagonal faces
The Next CEO of Stack OverflowIntuition about the faces in the connected planar graphs“faces” of a non-planar graphDraw a cubic planar graph with six faces of degree $4$ and one with $6$…Genus and faces of a graphHow to find a planar graph if I know that it has 7 faces with certain sizes?Number of vertices in hexagonal tiling of rectangleAttempting to understand what a “Face” in planar graph to count faces correctlyplanar graphs and number of facesCount of maximal sextic toroidal graphsFiniteness of regular planar simple graphs with their faces bounded by cycles of the same length
$begingroup$
How many are there non isotopic (in a sphere) embeddings of graphs with $n$ vertices, such that all faces are hexagons (including external face)? A given graph and its mirror image can be counted as one.
An example of such graph is presented below.
I suspect that there is no closed formula but maybe for $n=8,10,12$ there is such enumeration.
combinatorics graph-theory
asked 2 days ago
oldold
332111
$endgroup$
This question has an open bounty worth +50
reputation from old ending ending at 2019-04-05 17:14:44Z">in 7 days.
This question has not received enough attention.
add a comment |
$begingroup$
How many are there non isotopic (in a sphere) embeddings of graphs with $n$ vertices, such that all faces are hexagons (including external face)? A given graph and its mirror image can be counted as one.
An example of such graph is presented below.
I suspect that there is no closed formula but maybe for $n=8,10,12$ there is such enumeration.
combinatorics graph-theory
asked 2 days ago
oldold
332111
$endgroup$
This question has an open bounty worth +50
reputation from old ending ending at 2019-04-05 17:14:44Z">in 7 days.
This question has not received enough attention.
1
$begingroup$
What's your stance on chirality? The graph you've drawn has an opposite embedding, which can only be reached by an orientation-reversing map. Is that one or two embeddings in the count?
$endgroup$
– jmerry
7 hours ago
1
$begingroup$
Also, multigraphs. At 10 or more vertices, it's possible to set up a planar multigraph with more than one edge between the same pair of vertices. Is this allowed or not?
$endgroup$
– jmerry
7 hours ago
1
$begingroup$
A given graph and its mirror image can be counted as one. No multigraphs, as I consider them to have bigonal faces.
$endgroup$
– old
6 hours ago
add a comment |
$begingroup$
How many are there non isotopic (in a sphere) embeddings of graphs with $n$ vertices, such that all faces are hexagons (including external face)? A given graph and its mirror image can be counted as one.
An example of such graph is presented below.
I suspect that there is no closed formula but maybe for $n=8,10,12$ there is such enumeration.
combinatorics graph-theory
asked 2 days ago
oldold
332111
$endgroup$
How many are there non isotopic (in a sphere) embeddings of graphs with $n$ vertices, such that all faces are hexagons (including external face)? A given graph and its mirror image can be counted as one.
An example of such graph is presented below.
I suspect that there is no closed formula but maybe for $n=8,10,12$ there is such enumeration.
combinatorics graph-theory
combinatorics graph-theory
asked 2 days ago
oldold
332111
asked 2 days ago
oldold
332111
edited 6 hours ago
old
asked 2 days ago
oldold
332111
asked 2 days ago
oldold
332111
asked 2 days ago
oldold
332111
332111
This question has an open bounty worth +50
reputation from old ending ending at 2019-04-05 17:14:44Z">in 7 days.
This question has not received enough attention.
This question has an open bounty worth +50
reputation from old ending ending at 2019-04-05 17:14:44Z">in 7 days.
This question has not received enough attention.
1
$begingroup$
What's your stance on chirality? The graph you've drawn has an opposite embedding, which can only be reached by an orientation-reversing map. Is that one or two embeddings in the count?
$endgroup$
– jmerry
7 hours ago
1
$begingroup$
Also, multigraphs. At 10 or more vertices, it's possible to set up a planar multigraph with more than one edge between the same pair of vertices. Is this allowed or not?
$endgroup$
– jmerry
7 hours ago
1
$begingroup$
A given graph and its mirror image can be counted as one. No multigraphs, as I consider them to have bigonal faces.
$endgroup$
– old
6 hours ago
add a comment |
1
$begingroup$
What's your stance on chirality? The graph you've drawn has an opposite embedding, which can only be reached by an orientation-reversing map. Is that one or two embeddings in the count?
$endgroup$
– jmerry
7 hours ago
1
$begingroup$
Also, multigraphs. At 10 or more vertices, it's possible to set up a planar multigraph with more than one edge between the same pair of vertices. Is this allowed or not?
$endgroup$
– jmerry
7 hours ago
1
$begingroup$
A given graph and its mirror image can be counted as one. No multigraphs, as I consider them to have bigonal faces.
$endgroup$
– old
6 hours ago
1
1
$begingroup$
What's your stance on chirality? The graph you've drawn has an opposite embedding, which can only be reached by an orientation-reversing map. Is that one or two embeddings in the count?
$endgroup$
– jmerry
7 hours ago
$begingroup$
What's your stance on chirality? The graph you've drawn has an opposite embedding, which can only be reached by an orientation-reversing map. Is that one or two embeddings in the count?
$endgroup$
– jmerry
7 hours ago
1
1
$begingroup$
Also, multigraphs. At 10 or more vertices, it's possible to set up a planar multigraph with more than one edge between the same pair of vertices. Is this allowed or not?
$endgroup$
– jmerry
7 hours ago
$begingroup$
Also, multigraphs. At 10 or more vertices, it's possible to set up a planar multigraph with more than one edge between the same pair of vertices. Is this allowed or not?
$endgroup$
– jmerry
7 hours ago
1
1
$begingroup$
A given graph and its mirror image can be counted as one. No multigraphs, as I consider them to have bigonal faces.
$endgroup$
– old
6 hours ago
$begingroup$
A given graph and its mirror image can be counted as one. No multigraphs, as I consider them to have bigonal faces.
$endgroup$
– old
6 hours ago
add a comment |
0
active
oldest
votes
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1
$begingroup$
What's your stance on chirality? The graph you've drawn has an opposite embedding, which can only be reached by an orientation-reversing map. Is that one or two embeddings in the count?
$endgroup$
– jmerry
7 hours ago
1
$begingroup$
Also, multigraphs. At 10 or more vertices, it's possible to set up a planar multigraph with more than one edge between the same pair of vertices. Is this allowed or not?
$endgroup$
– jmerry
7 hours ago
1
$begingroup$
A given graph and its mirror image can be counted as one. No multigraphs, as I consider them to have bigonal faces.
$endgroup$
– old
6 hours ago