How to get the one-to-one correspondence of vertices between two graphs?

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I have two weighted isomorphic graphs below.The color of the edge represents the weight of the graph.Obviously,vertex a corresponds to vertex 1,b corresponds to 2 and c corresponds to 3.Here is the question.Suppose I have two more complicated weighted isomorphic graphs and I can make sure that there is only one unique isomorphism between them,how can I get the one-to-one correspondence of vertices between these two graphs.Thank you very much.
Click here to view the picture of two weighted isomorphic graphs

graph-theory matching-theory

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edited Aug 1 at 0:24

asked Jul 30 at 9:42

Yanjie Li

13

• 
  
  
  

  
  

  
  
  
  
  
  

  
  (1) Where are the weights? (2) Why couldn't the isomorphism be $a leftrightarrow 3, b leftrightarrow 2, c leftrightarrow 1$? What makes you think that there's the one-to-one correspondence rather than a one-to--one correspondence?
  – John Hughes
  Jul 30 at 9:44
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Sorry,it's my fault,I haven't express the question clearly.The color of the edge represents the weight of the graph.For example,the red color represent a weight of 10,and the green color represent a weight of 20.Thank you for your answer sincerely.
  – Yanjie Li
  Jul 31 at 0:26
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Actually,I also have a second question but I haven't asked.That is.If I have two weighted isomorphism graphs,how can I figure out how many one-to-one correspondences between them.Thank you again.
  – Yanjie Li
  Jul 31 at 1:07
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Since no one has yet answered your question, it's OK to edit it -- click the word "edit" beneath the question and fix things up. But in general, you should ask one question per question, and once someone has answered, you should avoid changing the question, because this makes the answer look silly. One last thing: in English, we say "Suppose I have two weighted isomorphic graphs. How can I figure out how many isomorphisms between them there are?" ('isomorphism' is a noun; 'isomorphic' is an adjective). I suspect that this second question is quite difficult.
  – John Hughes
  Jul 31 at 11:31
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for your advice,John.You are so kind.I will edit the first question again.And I will add a new question about the second one.
  – Yanjie Li
  Aug 1 at 0:09
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

I have two weighted isomorphic graphs below.The color of the edge represents the weight of the graph.Obviously,vertex a corresponds to vertex 1,b corresponds to 2 and c corresponds to 3.Here is the question.Suppose I have two more complicated weighted isomorphic graphs and I can make sure that there is only one unique isomorphism between them,how can I get the one-to-one correspondence of vertices between these two graphs.Thank you very much.
Click here to view the picture of two weighted isomorphic graphs

graph-theory matching-theory

share|cite|improve this question

edited Aug 1 at 0:24

asked Jul 30 at 9:42

Yanjie Li

13

• 
  
  
  

  
  

  
  
  
  
  
  

  
  (1) Where are the weights? (2) Why couldn't the isomorphism be $a leftrightarrow 3, b leftrightarrow 2, c leftrightarrow 1$? What makes you think that there's the one-to-one correspondence rather than a one-to--one correspondence?
  – John Hughes
  Jul 30 at 9:44
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Sorry,it's my fault,I haven't express the question clearly.The color of the edge represents the weight of the graph.For example,the red color represent a weight of 10,and the green color represent a weight of 20.Thank you for your answer sincerely.
  – Yanjie Li
  Jul 31 at 0:26
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Actually,I also have a second question but I haven't asked.That is.If I have two weighted isomorphism graphs,how can I figure out how many one-to-one correspondences between them.Thank you again.
  – Yanjie Li
  Jul 31 at 1:07
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Since no one has yet answered your question, it's OK to edit it -- click the word "edit" beneath the question and fix things up. But in general, you should ask one question per question, and once someone has answered, you should avoid changing the question, because this makes the answer look silly. One last thing: in English, we say "Suppose I have two weighted isomorphic graphs. How can I figure out how many isomorphisms between them there are?" ('isomorphism' is a noun; 'isomorphic' is an adjective). I suspect that this second question is quite difficult.
  – John Hughes
  Jul 31 at 11:31
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for your advice,John.You are so kind.I will edit the first question again.And I will add a new question about the second one.
  – Yanjie Li
  Aug 1 at 0:09
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

up vote
0
down vote

favorite

I have two weighted isomorphic graphs below.The color of the edge represents the weight of the graph.Obviously,vertex a corresponds to vertex 1,b corresponds to 2 and c corresponds to 3.Here is the question.Suppose I have two more complicated weighted isomorphic graphs and I can make sure that there is only one unique isomorphism between them,how can I get the one-to-one correspondence of vertices between these two graphs.Thank you very much.
Click here to view the picture of two weighted isomorphic graphs

graph-theory matching-theory

share|cite|improve this question

edited Aug 1 at 0:24

asked Jul 30 at 9:42

Yanjie Li

13

I have two weighted isomorphic graphs below.The color of the edge represents the weight of the graph.Obviously,vertex a corresponds to vertex 1,b corresponds to 2 and c corresponds to 3.Here is the question.Suppose I have two more complicated weighted isomorphic graphs and I can make sure that there is only one unique isomorphism between them,how can I get the one-to-one correspondence of vertices between these two graphs.Thank you very much.
Click here to view the picture of two weighted isomorphic graphs

graph-theory matching-theory

share|cite|improve this question

edited Aug 1 at 0:24

asked Jul 30 at 9:42

Yanjie Li

13

share|cite|improve this question

share|cite|improve this question

edited Aug 1 at 0:24

edited Aug 1 at 0:24

edited Aug 1 at 0:24

asked Jul 30 at 9:42

Yanjie Li

13

asked Jul 30 at 9:42

Yanjie Li

13

asked Jul 30 at 9:42

Yanjie Li

13

13

• 
  
  
  

  
  

  
  
  
  
  
  

  
  (1) Where are the weights? (2) Why couldn't the isomorphism be $a leftrightarrow 3, b leftrightarrow 2, c leftrightarrow 1$? What makes you think that there's the one-to-one correspondence rather than a one-to--one correspondence?
  – John Hughes
  Jul 30 at 9:44
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Sorry,it's my fault,I haven't express the question clearly.The color of the edge represents the weight of the graph.For example,the red color represent a weight of 10,and the green color represent a weight of 20.Thank you for your answer sincerely.
  – Yanjie Li
  Jul 31 at 0:26
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Actually,I also have a second question but I haven't asked.That is.If I have two weighted isomorphism graphs,how can I figure out how many one-to-one correspondences between them.Thank you again.
  – Yanjie Li
  Jul 31 at 1:07
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Since no one has yet answered your question, it's OK to edit it -- click the word "edit" beneath the question and fix things up. But in general, you should ask one question per question, and once someone has answered, you should avoid changing the question, because this makes the answer look silly. One last thing: in English, we say "Suppose I have two weighted isomorphic graphs. How can I figure out how many isomorphisms between them there are?" ('isomorphism' is a noun; 'isomorphic' is an adjective). I suspect that this second question is quite difficult.
  – John Hughes
  Jul 31 at 11:31
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for your advice,John.You are so kind.I will edit the first question again.And I will add a new question about the second one.
  – Yanjie Li
  Aug 1 at 0:09
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  (1) Where are the weights? (2) Why couldn't the isomorphism be $a leftrightarrow 3, b leftrightarrow 2, c leftrightarrow 1$? What makes you think that there's the one-to-one correspondence rather than a one-to--one correspondence?
  – John Hughes
  Jul 30 at 9:44
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Sorry,it's my fault,I haven't express the question clearly.The color of the edge represents the weight of the graph.For example,the red color represent a weight of 10,and the green color represent a weight of 20.Thank you for your answer sincerely.
  – Yanjie Li
  Jul 31 at 0:26
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Actually,I also have a second question but I haven't asked.That is.If I have two weighted isomorphism graphs,how can I figure out how many one-to-one correspondences between them.Thank you again.
  – Yanjie Li
  Jul 31 at 1:07
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Since no one has yet answered your question, it's OK to edit it -- click the word "edit" beneath the question and fix things up. But in general, you should ask one question per question, and once someone has answered, you should avoid changing the question, because this makes the answer look silly. One last thing: in English, we say "Suppose I have two weighted isomorphic graphs. How can I figure out how many isomorphisms between them there are?" ('isomorphism' is a noun; 'isomorphic' is an adjective). I suspect that this second question is quite difficult.
  – John Hughes
  Jul 31 at 11:31
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for your advice,John.You are so kind.I will edit the first question again.And I will add a new question about the second one.
  – Yanjie Li
  Aug 1 at 0:09
  

  
  
  
  

(1) Where are the weights? (2) Why couldn't the isomorphism be $a leftrightarrow 3, b leftrightarrow 2, c leftrightarrow 1$? What makes you think that there's the one-to-one correspondence rather than a one-to--one correspondence?
– John Hughes
Jul 30 at 9:44

(1) Where are the weights? (2) Why couldn't the isomorphism be $a leftrightarrow 3, b leftrightarrow 2, c leftrightarrow 1$? What makes you think that there's the one-to-one correspondence rather than a one-to--one correspondence?
– John Hughes
Jul 30 at 9:44

Sorry,it's my fault,I haven't express the question clearly.The color of the edge represents the weight of the graph.For example,the red color represent a weight of 10,and the green color represent a weight of 20.Thank you for your answer sincerely.
– Yanjie Li
Jul 31 at 0:26

Sorry,it's my fault,I haven't express the question clearly.The color of the edge represents the weight of the graph.For example,the red color represent a weight of 10,and the green color represent a weight of 20.Thank you for your answer sincerely.
– Yanjie Li
Jul 31 at 0:26

Actually,I also have a second question but I haven't asked.That is.If I have two weighted isomorphism graphs,how can I figure out how many one-to-one correspondences between them.Thank you again.
– Yanjie Li
Jul 31 at 1:07

Actually,I also have a second question but I haven't asked.That is.If I have two weighted isomorphism graphs,how can I figure out how many one-to-one correspondences between them.Thank you again.
– Yanjie Li
Jul 31 at 1:07

Since no one has yet answered your question, it's OK to edit it -- click the word "edit" beneath the question and fix things up. But in general, you should ask one question per question, and once someone has answered, you should avoid changing the question, because this makes the answer look silly. One last thing: in English, we say "Suppose I have two weighted isomorphic graphs. How can I figure out how many isomorphisms between them there are?" ('isomorphism' is a noun; 'isomorphic' is an adjective). I suspect that this second question is quite difficult.
– John Hughes
Jul 31 at 11:31

Since no one has yet answered your question, it's OK to edit it -- click the word "edit" beneath the question and fix things up. But in general, you should ask one question per question, and once someone has answered, you should avoid changing the question, because this makes the answer look silly. One last thing: in English, we say "Suppose I have two weighted isomorphic graphs. How can I figure out how many isomorphisms between them there are?" ('isomorphism' is a noun; 'isomorphic' is an adjective). I suspect that this second question is quite difficult.
– John Hughes
Jul 31 at 11:31

Thanks for your advice,John.You are so kind.I will edit the first question again.And I will add a new question about the second one.
– Yanjie Li
Aug 1 at 0:09

Thanks for your advice,John.You are so kind.I will edit the first question again.And I will add a new question about the second one.
– Yanjie Li
Aug 1 at 0:09

add a comment | 

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