What does it mean that a graph dual is not unique, because the dual depends on the particular embedding?
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
What does it mean that a graph dual is not unique, because the dual depends on the particular embedding?
I don't get what graph embeddings are and how they're related to the uniqueness of the dual.
Particularly, is drawing the dual meant to be done in planar sense? That one considers as if the graph was projected on to a plane? So one is able to cross edges once in only a particular way, whereas in a "space" representation I don't think the embedding would matter, since one'd always draw through the edges the same way.
graph-theory
add a comment |Â
up vote
0
down vote
favorite
What does it mean that a graph dual is not unique, because the dual depends on the particular embedding?
I don't get what graph embeddings are and how they're related to the uniqueness of the dual.
Particularly, is drawing the dual meant to be done in planar sense? That one considers as if the graph was projected on to a plane? So one is able to cross edges once in only a particular way, whereas in a "space" representation I don't think the embedding would matter, since one'd always draw through the edges the same way.
graph-theory
I think you calculate a dual (not the dual) by drawing a plane picture of a (planar) graph, then putting a dual vertex in each region. But there are different ways to draw the graph in the plane that lead to different duals. (Posted as a comment not an answer since I haven't worked out details.)
â Ethan Bolker
Aug 8 at 18:56
@EthanBolker That confuses the notion of the dual a bit though, doesn't it? Since there are many duals, then how do decide, which one to use?
â mavavilj
Aug 8 at 18:57
You can't decide that in advance. "The dual" is ambinguous. See en.wikipedia.org/wiki/Dual_graph#Uniqueness for a confirmation of my comment. There's an example there.
â Ethan Bolker
Aug 8 at 19:01
Interpretdual
as a function of the embedded graph, or the embedding itself, not as a function of the graph.
â user582578
Aug 8 at 19:08
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
What does it mean that a graph dual is not unique, because the dual depends on the particular embedding?
I don't get what graph embeddings are and how they're related to the uniqueness of the dual.
Particularly, is drawing the dual meant to be done in planar sense? That one considers as if the graph was projected on to a plane? So one is able to cross edges once in only a particular way, whereas in a "space" representation I don't think the embedding would matter, since one'd always draw through the edges the same way.
graph-theory
What does it mean that a graph dual is not unique, because the dual depends on the particular embedding?
I don't get what graph embeddings are and how they're related to the uniqueness of the dual.
Particularly, is drawing the dual meant to be done in planar sense? That one considers as if the graph was projected on to a plane? So one is able to cross edges once in only a particular way, whereas in a "space" representation I don't think the embedding would matter, since one'd always draw through the edges the same way.
graph-theory
edited Aug 8 at 18:56
asked Aug 8 at 18:52
mavavilj
2,470730
2,470730
I think you calculate a dual (not the dual) by drawing a plane picture of a (planar) graph, then putting a dual vertex in each region. But there are different ways to draw the graph in the plane that lead to different duals. (Posted as a comment not an answer since I haven't worked out details.)
â Ethan Bolker
Aug 8 at 18:56
@EthanBolker That confuses the notion of the dual a bit though, doesn't it? Since there are many duals, then how do decide, which one to use?
â mavavilj
Aug 8 at 18:57
You can't decide that in advance. "The dual" is ambinguous. See en.wikipedia.org/wiki/Dual_graph#Uniqueness for a confirmation of my comment. There's an example there.
â Ethan Bolker
Aug 8 at 19:01
Interpretdual
as a function of the embedded graph, or the embedding itself, not as a function of the graph.
â user582578
Aug 8 at 19:08
add a comment |Â
I think you calculate a dual (not the dual) by drawing a plane picture of a (planar) graph, then putting a dual vertex in each region. But there are different ways to draw the graph in the plane that lead to different duals. (Posted as a comment not an answer since I haven't worked out details.)
â Ethan Bolker
Aug 8 at 18:56
@EthanBolker That confuses the notion of the dual a bit though, doesn't it? Since there are many duals, then how do decide, which one to use?
â mavavilj
Aug 8 at 18:57
You can't decide that in advance. "The dual" is ambinguous. See en.wikipedia.org/wiki/Dual_graph#Uniqueness for a confirmation of my comment. There's an example there.
â Ethan Bolker
Aug 8 at 19:01
Interpretdual
as a function of the embedded graph, or the embedding itself, not as a function of the graph.
â user582578
Aug 8 at 19:08
I think you calculate a dual (not the dual) by drawing a plane picture of a (planar) graph, then putting a dual vertex in each region. But there are different ways to draw the graph in the plane that lead to different duals. (Posted as a comment not an answer since I haven't worked out details.)
â Ethan Bolker
Aug 8 at 18:56
I think you calculate a dual (not the dual) by drawing a plane picture of a (planar) graph, then putting a dual vertex in each region. But there are different ways to draw the graph in the plane that lead to different duals. (Posted as a comment not an answer since I haven't worked out details.)
â Ethan Bolker
Aug 8 at 18:56
@EthanBolker That confuses the notion of the dual a bit though, doesn't it? Since there are many duals, then how do decide, which one to use?
â mavavilj
Aug 8 at 18:57
@EthanBolker That confuses the notion of the dual a bit though, doesn't it? Since there are many duals, then how do decide, which one to use?
â mavavilj
Aug 8 at 18:57
You can't decide that in advance. "The dual" is ambinguous. See en.wikipedia.org/wiki/Dual_graph#Uniqueness for a confirmation of my comment. There's an example there.
â Ethan Bolker
Aug 8 at 19:01
You can't decide that in advance. "The dual" is ambinguous. See en.wikipedia.org/wiki/Dual_graph#Uniqueness for a confirmation of my comment. There's an example there.
â Ethan Bolker
Aug 8 at 19:01
Interpret
dual
as a function of the embedded graph, or the embedding itself, not as a function of the graph.â user582578
Aug 8 at 19:08
Interpret
dual
as a function of the embedded graph, or the embedding itself, not as a function of the graph.â user582578
Aug 8 at 19:08
add a comment |Â
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2876440%2fwhat-does-it-mean-that-a-graph-dual-is-not-unique-because-the-dual-depends-on-t%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
I think you calculate a dual (not the dual) by drawing a plane picture of a (planar) graph, then putting a dual vertex in each region. But there are different ways to draw the graph in the plane that lead to different duals. (Posted as a comment not an answer since I haven't worked out details.)
â Ethan Bolker
Aug 8 at 18:56
@EthanBolker That confuses the notion of the dual a bit though, doesn't it? Since there are many duals, then how do decide, which one to use?
â mavavilj
Aug 8 at 18:57
You can't decide that in advance. "The dual" is ambinguous. See en.wikipedia.org/wiki/Dual_graph#Uniqueness for a confirmation of my comment. There's an example there.
â Ethan Bolker
Aug 8 at 19:01
Interpret
dual
as a function of the embedded graph, or the embedding itself, not as a function of the graph.â user582578
Aug 8 at 19:08