Is there a way to make two different adjacency matrices (same size) have the same degree matrix?

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For the same set of vertices, there are two different topologies and edge weights. Therefore, we have two different adjacency matrices for the same vertices. Is it possible to make those two different adjacency matrices have the same degree matrix?

combinatorics matrices discrete-mathematics graph-theory optimization

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edited Jul 26 at 15:38

asked Jul 24 at 15:38

E.J.

475416

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  By "degree matrix" you mean degree sequence? If so, then yes, we can take the graphs of the pentagonal prism and Petersen's graph.
  – Parcly Taxel
  Jul 24 at 15:42
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @ParclyTaxel The definition of "degree matrix" is here en.wikipedia.org/wiki/Degree_matrix. Can you specify how to do that or any references?
  – E.J.
  Jul 24 at 15:46
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  The degree matrix is a diagonal matrix and its diagonal forms the degree sequence.
  – Parcly Taxel
  Jul 24 at 15:50
  

  
  
  
  

add a comment | 

up vote
1
down vote

favorite

For the same set of vertices, there are two different topologies and edge weights. Therefore, we have two different adjacency matrices for the same vertices. Is it possible to make those two different adjacency matrices have the same degree matrix?

combinatorics matrices discrete-mathematics graph-theory optimization

share|cite|improve this question

edited Jul 26 at 15:38

asked Jul 24 at 15:38

E.J.

475416

• 
  
  
  

  
  

  
  
  
  
  
  

  
  By "degree matrix" you mean degree sequence? If so, then yes, we can take the graphs of the pentagonal prism and Petersen's graph.
  – Parcly Taxel
  Jul 24 at 15:42
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @ParclyTaxel The definition of "degree matrix" is here en.wikipedia.org/wiki/Degree_matrix. Can you specify how to do that or any references?
  – E.J.
  Jul 24 at 15:46
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  The degree matrix is a diagonal matrix and its diagonal forms the degree sequence.
  – Parcly Taxel
  Jul 24 at 15:50
  

  
  
  
  

add a comment | 

up vote
1
down vote

favorite

up vote
1
down vote

favorite

For the same set of vertices, there are two different topologies and edge weights. Therefore, we have two different adjacency matrices for the same vertices. Is it possible to make those two different adjacency matrices have the same degree matrix?

combinatorics matrices discrete-mathematics graph-theory optimization

share|cite|improve this question

edited Jul 26 at 15:38

asked Jul 24 at 15:38

E.J.

475416

For the same set of vertices, there are two different topologies and edge weights. Therefore, we have two different adjacency matrices for the same vertices. Is it possible to make those two different adjacency matrices have the same degree matrix?

combinatorics matrices discrete-mathematics graph-theory optimization

share|cite|improve this question

edited Jul 26 at 15:38

asked Jul 24 at 15:38

E.J.

475416

share|cite|improve this question

share|cite|improve this question

edited Jul 26 at 15:38

edited Jul 26 at 15:38

edited Jul 26 at 15:38

asked Jul 24 at 15:38

E.J.

475416

asked Jul 24 at 15:38

E.J.

475416

asked Jul 24 at 15:38

E.J.

475416

475416

• 
  
  
  

  
  

  
  
  
  
  
  

  
  By "degree matrix" you mean degree sequence? If so, then yes, we can take the graphs of the pentagonal prism and Petersen's graph.
  – Parcly Taxel
  Jul 24 at 15:42
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @ParclyTaxel The definition of "degree matrix" is here en.wikipedia.org/wiki/Degree_matrix. Can you specify how to do that or any references?
  – E.J.
  Jul 24 at 15:46
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  The degree matrix is a diagonal matrix and its diagonal forms the degree sequence.
  – Parcly Taxel
  Jul 24 at 15:50
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  By "degree matrix" you mean degree sequence? If so, then yes, we can take the graphs of the pentagonal prism and Petersen's graph.
  – Parcly Taxel
  Jul 24 at 15:42
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @ParclyTaxel The definition of "degree matrix" is here en.wikipedia.org/wiki/Degree_matrix. Can you specify how to do that or any references?
  – E.J.
  Jul 24 at 15:46
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  The degree matrix is a diagonal matrix and its diagonal forms the degree sequence.
  – Parcly Taxel
  Jul 24 at 15:50
  

  
  
  
  

By "degree matrix" you mean degree sequence? If so, then yes, we can take the graphs of the pentagonal prism and Petersen's graph.
– Parcly Taxel
Jul 24 at 15:42

By "degree matrix" you mean degree sequence? If so, then yes, we can take the graphs of the pentagonal prism and Petersen's graph.
– Parcly Taxel
Jul 24 at 15:42

@ParclyTaxel The definition of "degree matrix" is here en.wikipedia.org/wiki/Degree_matrix. Can you specify how to do that or any references?
– E.J.
Jul 24 at 15:46

@ParclyTaxel The definition of "degree matrix" is here en.wikipedia.org/wiki/Degree_matrix. Can you specify how to do that or any references?
– E.J.
Jul 24 at 15:46

The degree matrix is a diagonal matrix and its diagonal forms the degree sequence.
– Parcly Taxel
Jul 24 at 15:50

The degree matrix is a diagonal matrix and its diagonal forms the degree sequence.
– Parcly Taxel
Jul 24 at 15:50

add a comment | 

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It is certainly possible. Note that the idea of a degree matrix can be represented more concisely by a degree sequence, since a degree matrix is diagonal.

For an explicit example of two graphs with different adjacency matrices but the same degree matrix, consider:

• the 1-skeleton of the pentagonal prism (its vertices and edges), which has girth 4


• the Petersen graph of girth 5

Both of them have different adjacency matrices, but the same degree matrix of three times the identity matrix of size 10 (i.e. a degree sequence of ten threes).

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answered Jul 24 at 15:51

Parcly Taxel

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It is certainly possible. Note that the idea of a degree matrix can be represented more concisely by a degree sequence, since a degree matrix is diagonal.

For an explicit example of two graphs with different adjacency matrices but the same degree matrix, consider:

• the 1-skeleton of the pentagonal prism (its vertices and edges), which has girth 4


• the Petersen graph of girth 5

Both of them have different adjacency matrices, but the same degree matrix of three times the identity matrix of size 10 (i.e. a degree sequence of ten threes).

share|cite|improve this answer

answered Jul 24 at 15:51

Parcly Taxel

33.5k136588

add a comment | 

up vote
3
down vote

It is certainly possible. Note that the idea of a degree matrix can be represented more concisely by a degree sequence, since a degree matrix is diagonal.

For an explicit example of two graphs with different adjacency matrices but the same degree matrix, consider:

• the 1-skeleton of the pentagonal prism (its vertices and edges), which has girth 4


• the Petersen graph of girth 5

Both of them have different adjacency matrices, but the same degree matrix of three times the identity matrix of size 10 (i.e. a degree sequence of ten threes).

share|cite|improve this answer

answered Jul 24 at 15:51

Parcly Taxel

33.5k136588

add a comment | 

up vote
3
down vote

up vote
3
down vote

It is certainly possible. Note that the idea of a degree matrix can be represented more concisely by a degree sequence, since a degree matrix is diagonal.

For an explicit example of two graphs with different adjacency matrices but the same degree matrix, consider:

• the 1-skeleton of the pentagonal prism (its vertices and edges), which has girth 4


• the Petersen graph of girth 5

Both of them have different adjacency matrices, but the same degree matrix of three times the identity matrix of size 10 (i.e. a degree sequence of ten threes).

share|cite|improve this answer

answered Jul 24 at 15:51

Parcly Taxel

33.5k136588

It is certainly possible. Note that the idea of a degree matrix can be represented more concisely by a degree sequence, since a degree matrix is diagonal.

For an explicit example of two graphs with different adjacency matrices but the same degree matrix, consider:

• the 1-skeleton of the pentagonal prism (its vertices and edges), which has girth 4


• the Petersen graph of girth 5

Both of them have different adjacency matrices, but the same degree matrix of three times the identity matrix of size 10 (i.e. a degree sequence of ten threes).

share|cite|improve this answer

answered Jul 24 at 15:51

Parcly Taxel

33.5k136588

share|cite|improve this answer

share|cite|improve this answer

answered Jul 24 at 15:51

Parcly Taxel

33.5k136588

answered Jul 24 at 15:51

Parcly Taxel

33.5k136588

answered Jul 24 at 15:51

Parcly Taxel

33.5k136588

33.5k136588

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add a comment | 

 

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