I'm working on an assignment and I have no idea how to start on it. I was wondering if you could at least...
-1
For each of the 11 different isomorphism classes of graphs on 4 vertices presented in class
write down the Laplacian matrix and calculate the characteristic polynomial, characteristic equation and
the eigenvalues for each isomorphism class.
linear-algebra graph-theory
edited Nov 28 at 19:26
Bernard
117k637111
asked Nov 28 at 18:27
cheyanne pressley
1
|
show 1 more comment
-1
For each of the 11 different isomorphism classes of graphs on 4 vertices presented in class
write down the Laplacian matrix and calculate the characteristic polynomial, characteristic equation and
the eigenvalues for each isomorphism class.
linear-algebra graph-theory
edited Nov 28 at 19:26
Bernard
117k637111
asked Nov 28 at 18:27
cheyanne pressley
1
4
Start by writing down a member of the first isomorphism class, and then its Laplacian matrix...
– Robert Israel
Nov 28 at 18:31
Can you find $11$ isomorphism classes? Can you verify that there are no others? Do you know how to construct the Laplacian? "I have no idea" is surely inaccurate, and it doesn't let us know where your difficulty lies.
– saulspatz
Nov 28 at 18:33
mathworld.wolfram.com/SimpleGraph.html
– cheyanne pressley
Nov 28 at 18:46
2
Please change the thread title to something more descriptive.
– Blazej
Nov 28 at 18:53
2
Do you know the definitions of "Laplacian matrix (of a graph)", "characteristic polynomial", "characteristic equation", and "eigenvalue"? If not, then your first step is to look them up, since you surely can't do the problem without knowing what it means. If you do know the definitions, then you'll need to clarify (in your question) where you're encountering difficulty applying those defintiions.
– Andreas Blass
Nov 28 at 21:24
|
show 1 more comment
-1
-1
-1
For each of the 11 different isomorphism classes of graphs on 4 vertices presented in class
write down the Laplacian matrix and calculate the characteristic polynomial, characteristic equation and
the eigenvalues for each isomorphism class.
linear-algebra graph-theory
edited Nov 28 at 19:26
Bernard
117k637111
asked Nov 28 at 18:27
cheyanne pressley
1
For each of the 11 different isomorphism classes of graphs on 4 vertices presented in class
write down the Laplacian matrix and calculate the characteristic polynomial, characteristic equation and
the eigenvalues for each isomorphism class.
linear-algebra graph-theory
linear-algebra graph-theory
edited Nov 28 at 19:26
Bernard
117k637111
asked Nov 28 at 18:27
cheyanne pressley
1
edited Nov 28 at 19:26
Bernard
117k637111
asked Nov 28 at 18:27
cheyanne pressley
1
edited Nov 28 at 19:26
Bernard
117k637111
edited Nov 28 at 19:26
Bernard
117k637111
edited Nov 28 at 19:26
Bernard
117k637111
117k637111
asked Nov 28 at 18:27
cheyanne pressley
1
asked Nov 28 at 18:27
cheyanne pressley
1
asked Nov 28 at 18:27
cheyanne pressley
1
1
4
Start by writing down a member of the first isomorphism class, and then its Laplacian matrix...
– Robert Israel
Nov 28 at 18:31
Can you find $11$ isomorphism classes? Can you verify that there are no others? Do you know how to construct the Laplacian? "I have no idea" is surely inaccurate, and it doesn't let us know where your difficulty lies.
– saulspatz
Nov 28 at 18:33
mathworld.wolfram.com/SimpleGraph.html
– cheyanne pressley
Nov 28 at 18:46
2
Please change the thread title to something more descriptive.
– Blazej
Nov 28 at 18:53
2
Do you know the definitions of "Laplacian matrix (of a graph)", "characteristic polynomial", "characteristic equation", and "eigenvalue"? If not, then your first step is to look them up, since you surely can't do the problem without knowing what it means. If you do know the definitions, then you'll need to clarify (in your question) where you're encountering difficulty applying those defintiions.
– Andreas Blass
Nov 28 at 21:24
|
show 1 more comment
4
Start by writing down a member of the first isomorphism class, and then its Laplacian matrix...
– Robert Israel
Nov 28 at 18:31
Can you find $11$ isomorphism classes? Can you verify that there are no others? Do you know how to construct the Laplacian? "I have no idea" is surely inaccurate, and it doesn't let us know where your difficulty lies.
– saulspatz
Nov 28 at 18:33
mathworld.wolfram.com/SimpleGraph.html
– cheyanne pressley
Nov 28 at 18:46
2
Please change the thread title to something more descriptive.
– Blazej
Nov 28 at 18:53
2
Do you know the definitions of "Laplacian matrix (of a graph)", "characteristic polynomial", "characteristic equation", and "eigenvalue"? If not, then your first step is to look them up, since you surely can't do the problem without knowing what it means. If you do know the definitions, then you'll need to clarify (in your question) where you're encountering difficulty applying those defintiions.
– Andreas Blass
Nov 28 at 21:24
4
4
Start by writing down a member of the first isomorphism class, and then its Laplacian matrix...
– Robert Israel
Nov 28 at 18:31
Start by writing down a member of the first isomorphism class, and then its Laplacian matrix...
– Robert Israel
Nov 28 at 18:31
Can you find $11$ isomorphism classes? Can you verify that there are no others? Do you know how to construct the Laplacian? "I have no idea" is surely inaccurate, and it doesn't let us know where your difficulty lies.
– saulspatz
Nov 28 at 18:33
Can you find $11$ isomorphism classes? Can you verify that there are no others? Do you know how to construct the Laplacian? "I have no idea" is surely inaccurate, and it doesn't let us know where your difficulty lies.
– saulspatz
Nov 28 at 18:33
mathworld.wolfram.com/SimpleGraph.html
– cheyanne pressley
Nov 28 at 18:46
mathworld.wolfram.com/SimpleGraph.html
– cheyanne pressley
Nov 28 at 18:46
2
2
Please change the thread title to something more descriptive.
– Blazej
Nov 28 at 18:53
Please change the thread title to something more descriptive.
– Blazej
Nov 28 at 18:53
2
2
Do you know the definitions of "Laplacian matrix (of a graph)", "characteristic polynomial", "characteristic equation", and "eigenvalue"? If not, then your first step is to look them up, since you surely can't do the problem without knowing what it means. If you do know the definitions, then you'll need to clarify (in your question) where you're encountering difficulty applying those defintiions.
– Andreas Blass
Nov 28 at 21:24
Do you know the definitions of "Laplacian matrix (of a graph)", "characteristic polynomial", "characteristic equation", and "eigenvalue"? If not, then your first step is to look them up, since you surely can't do the problem without knowing what it means. If you do know the definitions, then you'll need to clarify (in your question) where you're encountering difficulty applying those defintiions.
– Andreas Blass
Nov 28 at 21:24
|
show 1 more comment
1 Answer
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I'm not sure what if characteristic polynomial is the same as characteristic equation, but I computed for two classes.
answered Nov 30 at 23:44
mathnoob
1,775322
add a comment |
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I'm not sure what if characteristic polynomial is the same as characteristic equation, but I computed for two classes.
answered Nov 30 at 23:44
mathnoob
1,775322
add a comment |
0
I'm not sure what if characteristic polynomial is the same as characteristic equation, but I computed for two classes.
answered Nov 30 at 23:44
mathnoob
1,775322
add a comment |
0
0
0
I'm not sure what if characteristic polynomial is the same as characteristic equation, but I computed for two classes.
answered Nov 30 at 23:44
mathnoob
1,775322
I'm not sure what if characteristic polynomial is the same as characteristic equation, but I computed for two classes.
answered Nov 30 at 23:44
mathnoob
1,775322
answered Nov 30 at 23:44
mathnoob
1,775322
answered Nov 30 at 23:44
mathnoob
1,775322
answered Nov 30 at 23:44
mathnoob
1,775322
1,775322
add a comment |
add a comment |
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4
Start by writing down a member of the first isomorphism class, and then its Laplacian matrix...
– Robert Israel
Nov 28 at 18:31
Can you find $11$ isomorphism classes? Can you verify that there are no others? Do you know how to construct the Laplacian? "I have no idea" is surely inaccurate, and it doesn't let us know where your difficulty lies.
– saulspatz
Nov 28 at 18:33
mathworld.wolfram.com/SimpleGraph.html
– cheyanne pressley
Nov 28 at 18:46
2
Please change the thread title to something more descriptive.
– Blazej
Nov 28 at 18:53
2
Do you know the definitions of "Laplacian matrix (of a graph)", "characteristic polynomial", "characteristic equation", and "eigenvalue"? If not, then your first step is to look them up, since you surely can't do the problem without knowing what it means. If you do know the definitions, then you'll need to clarify (in your question) where you're encountering difficulty applying those defintiions.
– Andreas Blass
Nov 28 at 21:24