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Calculate the resistance between 2 adjacent nodes on a shape using graph theory

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In shapes like regular octahedron or dodecahedron, how can Graph Theory be used to calculate the resistance between two adjacent vertices? All edges are assumed to have unit resistance. Is there anything above the usual way to approach physics problems about cicuits?

graph-theory physics

share|cite|improve this question

edited 2 days ago

Lord Shark the Unknown

106k1161133

asked Jan 14 '16 at 8:26

Aritra DasAritra Das

2,06231433

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Depends on how you define "resistance"...
  $endgroup$
  – 5xum
  Jan 14 '16 at 8:27
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @5xum Now is it okay?
  $endgroup$
  – Aritra Das
  Jan 14 '16 at 8:30
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  So are we talking electrical resistance here?
  $endgroup$
  – 5xum
  Jan 14 '16 at 8:33
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @5xum Yes, or resistance distance as stated in this link: en.wikipedia.org/wiki/Resistance_distance
  $endgroup$
  – Aritra Das
  Jan 14 '16 at 8:34
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Are you familiar with the basics like serial and parallel resistance? Is this an exercise with a known nice solution or did you make that up yourself?
  $endgroup$
  – GDumphart
  Jan 14 '16 at 8:42
  

  
  
  
  

 | 
show 2 more comments

6

1

$begingroup$

In shapes like regular octahedron or dodecahedron, how can Graph Theory be used to calculate the resistance between two adjacent vertices? All edges are assumed to have unit resistance. Is there anything above the usual way to approach physics problems about cicuits?

graph-theory physics

share|cite|improve this question

edited 2 days ago

Lord Shark the Unknown

106k1161133

asked Jan 14 '16 at 8:26

Aritra DasAritra Das

2,06231433

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Depends on how you define "resistance"...
  $endgroup$
  – 5xum
  Jan 14 '16 at 8:27
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @5xum Now is it okay?
  $endgroup$
  – Aritra Das
  Jan 14 '16 at 8:30
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  So are we talking electrical resistance here?
  $endgroup$
  – 5xum
  Jan 14 '16 at 8:33
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @5xum Yes, or resistance distance as stated in this link: en.wikipedia.org/wiki/Resistance_distance
  $endgroup$
  – Aritra Das
  Jan 14 '16 at 8:34
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Are you familiar with the basics like serial and parallel resistance? Is this an exercise with a known nice solution or did you make that up yourself?
  $endgroup$
  – GDumphart
  Jan 14 '16 at 8:42
  

  
  
  
  

 | 
show 2 more comments

$begingroup$

In shapes like regular octahedron or dodecahedron, how can Graph Theory be used to calculate the resistance between two adjacent vertices? All edges are assumed to have unit resistance. Is there anything above the usual way to approach physics problems about cicuits?

graph-theory physics

share|cite|improve this question

edited 2 days ago

Lord Shark the Unknown

106k1161133

asked Jan 14 '16 at 8:26

Aritra DasAritra Das

2,06231433

$endgroup$

share|cite|improve this question

edited 2 days ago

Lord Shark the Unknown

106k1161133

asked Jan 14 '16 at 8:26

Aritra DasAritra Das

2,06231433

share|cite|improve this question

edited 2 days ago

Lord Shark the Unknown

106k1161133

asked Jan 14 '16 at 8:26

Aritra DasAritra Das

2,06231433

edited 2 days ago

Lord Shark the Unknown

106k1161133

edited 2 days ago

Lord Shark the Unknown

106k1161133

asked Jan 14 '16 at 8:26

Aritra DasAritra Das

2,06231433

asked Jan 14 '16 at 8:26

Aritra DasAritra Das

2,06231433