Different planar graphs with the same number of vertices and faces [on hold]
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
asked 16 hours ago
Rustam Mamin
61
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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.
add a comment |
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
asked 16 hours ago
Rustam Mamin
61
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
add a comment |
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
asked 16 hours ago
Rustam Mamin
61
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
asked 16 hours ago
Rustam Mamin
61
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.
asked 16 hours ago
Rustam Mamin
61
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.
edited 8 hours ago
asked 16 hours ago
Rustam Mamin
61
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.
asked 16 hours ago
Rustam Mamin
61
asked 16 hours ago
Rustam Mamin
61
61
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.
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
add a comment |
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
add a comment |
1 Answer
1
active
oldest
votes
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).
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.
answered 7 hours ago
Ankit Kumar
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
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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).
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.
answered 7 hours ago
Ankit Kumar
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
add a comment |
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).
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.
answered 7 hours ago
Ankit Kumar
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
add a comment |
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).
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.
answered 7 hours ago
Ankit Kumar
1,639119
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).
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.
answered 7 hours ago
Ankit Kumar
1,639119
answered 7 hours ago
Ankit Kumar
1,639119
answered 7 hours ago
Ankit Kumar
1,639119
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
add a comment |
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
add a comment |
1
The title and text are different questions.
– Don Thousand
16 hours ago