Different planar graphs with the same number of vertices and faces [on hold]

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Good time of the day!
Is there example of two different planar graphs with the same number of vertices and faces?






graph-theory planar-graph







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put on hold as off-topic by Gregory J. Puleo, mrtaurho, Saad, José Carlos Santos, Lord_Farin 3 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Gregory J. Puleo, mrtaurho, Saad, José Carlos Santos, Lord_Farin

If this question can be reworded to fit the rules in the help center, please edit the question.









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    The title and text are different questions.
    – Don Thousand
    16 hours ago
















0














Good time of the day!
Is there example of two different planar graphs with the same number of vertices and faces?






graph-theory planar-graph







share|cite|improve this question









New contributor




Rustam Mamin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











put on hold as off-topic by Gregory J. Puleo, mrtaurho, Saad, José Carlos Santos, Lord_Farin 3 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Gregory J. Puleo, mrtaurho, Saad, José Carlos Santos, Lord_Farin

If this question can be reworded to fit the rules in the help center, please edit the question.









  • 1




    The title and text are different questions.
    – Don Thousand
    16 hours ago














0












0








0







Good time of the day!
Is there example of two different planar graphs with the same number of vertices and faces?






graph-theory planar-graph







share|cite|improve this question









New contributor




Rustam Mamin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











Good time of the day!
Is there example of two different planar graphs with the same number of vertices and faces?






graph-theory planar-graph




graph-theory planar-graph






share|cite|improve this question









New contributor




Rustam Mamin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question









New contributor




Rustam Mamin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




share|cite|improve this question








edited 8 hours ago





















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Rustam Mamin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked 16 hours ago









Rustam Mamin

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New contributor




Rustam Mamin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor





Rustam Mamin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Rustam Mamin is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




put on hold as off-topic by Gregory J. Puleo, mrtaurho, Saad, José Carlos Santos, Lord_Farin 3 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Gregory J. Puleo, mrtaurho, Saad, José Carlos Santos, Lord_Farin

If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by Gregory J. Puleo, mrtaurho, Saad, José Carlos Santos, Lord_Farin 3 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Gregory J. Puleo, mrtaurho, Saad, José Carlos Santos, Lord_Farin

If this question can be reworded to fit the rules in the help center, please edit the question.








  • 1




    The title and text are different questions.
    – Don Thousand
    16 hours ago














  • 1




    The title and text are different questions.
    – Don Thousand
    16 hours ago








1




1




The title and text are different questions.
– Don Thousand
16 hours ago




The title and text are different questions.
– Don Thousand
16 hours ago










1 Answer
1






active

oldest

votes


















1














Well yeah! Let $f=$ no. of faces, $v=$ no. of vertices and $e=$ number of egdes. Then, by Euler's formula, $$v+f-e=2$$
So, same $f$ and $v$ imply same $v$ and $e$ (did this just because I'm more comfortable with edges than faces).



enter image description here



enter image description here



Note that both of these graphs are planar and are non-isomorphic since the upper graph has a vertex of degree 4 while the lower one doesn't.






share|cite|improve this answer





















  • Thank you. But what about non-isomorphic graphs with the same number of vertices, edges and faces?
    – Rustam Mamin
    6 hours ago










  • @RustamMamin Can you explain a bit what you are asking?
    – Ankit Kumar
    5 hours ago










  • Different planar graphs with the same number of vertices, faces and edges.
    – Rustam Mamin
    5 hours ago










  • The graphs I've made are different right? And they have same no of f, e and v
    – Ankit Kumar
    5 hours ago


















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









1














Well yeah! Let $f=$ no. of faces, $v=$ no. of vertices and $e=$ number of egdes. Then, by Euler's formula, $$v+f-e=2$$
So, same $f$ and $v$ imply same $v$ and $e$ (did this just because I'm more comfortable with edges than faces).



enter image description here



enter image description here



Note that both of these graphs are planar and are non-isomorphic since the upper graph has a vertex of degree 4 while the lower one doesn't.






share|cite|improve this answer





















  • Thank you. But what about non-isomorphic graphs with the same number of vertices, edges and faces?
    – Rustam Mamin
    6 hours ago










  • @RustamMamin Can you explain a bit what you are asking?
    – Ankit Kumar
    5 hours ago










  • Different planar graphs with the same number of vertices, faces and edges.
    – Rustam Mamin
    5 hours ago










  • The graphs I've made are different right? And they have same no of f, e and v
    – Ankit Kumar
    5 hours ago
















1














Well yeah! Let $f=$ no. of faces, $v=$ no. of vertices and $e=$ number of egdes. Then, by Euler's formula, $$v+f-e=2$$
So, same $f$ and $v$ imply same $v$ and $e$ (did this just because I'm more comfortable with edges than faces).



enter image description here



enter image description here



Note that both of these graphs are planar and are non-isomorphic since the upper graph has a vertex of degree 4 while the lower one doesn't.






share|cite|improve this answer





















  • Thank you. But what about non-isomorphic graphs with the same number of vertices, edges and faces?
    – Rustam Mamin
    6 hours ago










  • @RustamMamin Can you explain a bit what you are asking?
    – Ankit Kumar
    5 hours ago










  • Different planar graphs with the same number of vertices, faces and edges.
    – Rustam Mamin
    5 hours ago










  • The graphs I've made are different right? And they have same no of f, e and v
    – Ankit Kumar
    5 hours ago














1












1








1






Well yeah! Let $f=$ no. of faces, $v=$ no. of vertices and $e=$ number of egdes. Then, by Euler's formula, $$v+f-e=2$$
So, same $f$ and $v$ imply same $v$ and $e$ (did this just because I'm more comfortable with edges than faces).



enter image description here



enter image description here



Note that both of these graphs are planar and are non-isomorphic since the upper graph has a vertex of degree 4 while the lower one doesn't.






share|cite|improve this answer












Well yeah! Let $f=$ no. of faces, $v=$ no. of vertices and $e=$ number of egdes. Then, by Euler's formula, $$v+f-e=2$$
So, same $f$ and $v$ imply same $v$ and $e$ (did this just because I'm more comfortable with edges than faces).



enter image description here



enter image description here



Note that both of these graphs are planar and are non-isomorphic since the upper graph has a vertex of degree 4 while the lower one doesn't.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered 7 hours ago









Ankit Kumar

1,639119




1,639119












  • Thank you. But what about non-isomorphic graphs with the same number of vertices, edges and faces?
    – Rustam Mamin
    6 hours ago










  • @RustamMamin Can you explain a bit what you are asking?
    – Ankit Kumar
    5 hours ago










  • Different planar graphs with the same number of vertices, faces and edges.
    – Rustam Mamin
    5 hours ago










  • The graphs I've made are different right? And they have same no of f, e and v
    – Ankit Kumar
    5 hours ago


















  • Thank you. But what about non-isomorphic graphs with the same number of vertices, edges and faces?
    – Rustam Mamin
    6 hours ago










  • @RustamMamin Can you explain a bit what you are asking?
    – Ankit Kumar
    5 hours ago










  • Different planar graphs with the same number of vertices, faces and edges.
    – Rustam Mamin
    5 hours ago










  • The graphs I've made are different right? And they have same no of f, e and v
    – Ankit Kumar
    5 hours ago
















Thank you. But what about non-isomorphic graphs with the same number of vertices, edges and faces?
– Rustam Mamin
6 hours ago




Thank you. But what about non-isomorphic graphs with the same number of vertices, edges and faces?
– Rustam Mamin
6 hours ago












@RustamMamin Can you explain a bit what you are asking?
– Ankit Kumar
5 hours ago




@RustamMamin Can you explain a bit what you are asking?
– Ankit Kumar
5 hours ago












Different planar graphs with the same number of vertices, faces and edges.
– Rustam Mamin
5 hours ago




Different planar graphs with the same number of vertices, faces and edges.
– Rustam Mamin
5 hours ago












The graphs I've made are different right? And they have same no of f, e and v
– Ankit Kumar
5 hours ago




The graphs I've made are different right? And they have same no of f, e and v
– Ankit Kumar
5 hours ago



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