Tensor Product of Graphs and Eigenvalues

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Sorry if langauge is not so clear, I don't know very well the excat translation of terminology to English.



Question:
$G_1,G_2$ are undirected simple/strict graphs.
$A_G_1, A_G_2$ are adjacency matrixes of the graphs above.
1. If $alpha$ is an eigenvalue of $A_G_1$,and $beta$ is an eigenvalue of $A_G_2$.
then prove that $E * E'$ is an eigenvalue of $A_G_1 otimes G_2$



  1. G is undricted simple/strict graph, $omega(G)$ is the second biggest eigenvalue in it's absolute value for the normalized adjacency matrix of graph G, prove :
    $omega(G_1 otimes G_2) = maxomega(G_1),omega(G_2)$

I'm preety clueless about this subject so you can be extra informative on how to solve it, I'll be grateful.
Thank you!.




eigenvalues-eigenvectors tensor-products




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  • Welcome to MSE. It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures.
    – José Carlos Santos
    Jul 30 at 10:13










  • Already did, Thank you for enlighting me.
    – AmitBL
    Jul 30 at 10:33














up vote
0
down vote

favorite












Sorry if langauge is not so clear, I don't know very well the excat translation of terminology to English.



Question:
$G_1,G_2$ are undirected simple/strict graphs.
$A_G_1, A_G_2$ are adjacency matrixes of the graphs above.
1. If $alpha$ is an eigenvalue of $A_G_1$,and $beta$ is an eigenvalue of $A_G_2$.
then prove that $E * E'$ is an eigenvalue of $A_G_1 otimes G_2$



  1. G is undricted simple/strict graph, $omega(G)$ is the second biggest eigenvalue in it's absolute value for the normalized adjacency matrix of graph G, prove :
    $omega(G_1 otimes G_2) = maxomega(G_1),omega(G_2)$

I'm preety clueless about this subject so you can be extra informative on how to solve it, I'll be grateful.
Thank you!.




eigenvalues-eigenvectors tensor-products




share|cite|improve this question





















  • Welcome to MSE. It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures.
    – José Carlos Santos
    Jul 30 at 10:13










  • Already did, Thank you for enlighting me.
    – AmitBL
    Jul 30 at 10:33












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Sorry if langauge is not so clear, I don't know very well the excat translation of terminology to English.



Question:
$G_1,G_2$ are undirected simple/strict graphs.
$A_G_1, A_G_2$ are adjacency matrixes of the graphs above.
1. If $alpha$ is an eigenvalue of $A_G_1$,and $beta$ is an eigenvalue of $A_G_2$.
then prove that $E * E'$ is an eigenvalue of $A_G_1 otimes G_2$



  1. G is undricted simple/strict graph, $omega(G)$ is the second biggest eigenvalue in it's absolute value for the normalized adjacency matrix of graph G, prove :
    $omega(G_1 otimes G_2) = maxomega(G_1),omega(G_2)$

I'm preety clueless about this subject so you can be extra informative on how to solve it, I'll be grateful.
Thank you!.




eigenvalues-eigenvectors tensor-products




share|cite|improve this question













Sorry if langauge is not so clear, I don't know very well the excat translation of terminology to English.



Question:
$G_1,G_2$ are undirected simple/strict graphs.
$A_G_1, A_G_2$ are adjacency matrixes of the graphs above.
1. If $alpha$ is an eigenvalue of $A_G_1$,and $beta$ is an eigenvalue of $A_G_2$.
then prove that $E * E'$ is an eigenvalue of $A_G_1 otimes G_2$



  1. G is undricted simple/strict graph, $omega(G)$ is the second biggest eigenvalue in it's absolute value for the normalized adjacency matrix of graph G, prove :
    $omega(G_1 otimes G_2) = maxomega(G_1),omega(G_2)$

I'm preety clueless about this subject so you can be extra informative on how to solve it, I'll be grateful.
Thank you!.





eigenvalues-eigenvectors tensor-products





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 30 at 10:32
























asked Jul 30 at 10:08









AmitBL

61




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  • Welcome to MSE. It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures.
    – José Carlos Santos
    Jul 30 at 10:13










  • Already did, Thank you for enlighting me.
    – AmitBL
    Jul 30 at 10:33
















  • Welcome to MSE. It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures.
    – José Carlos Santos
    Jul 30 at 10:13










  • Already did, Thank you for enlighting me.
    – AmitBL
    Jul 30 at 10:33















Welcome to MSE. It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures.
– José Carlos Santos
Jul 30 at 10:13




Welcome to MSE. It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures.
– José Carlos Santos
Jul 30 at 10:13












Already did, Thank you for enlighting me.
– AmitBL
Jul 30 at 10:33




Already did, Thank you for enlighting me.
– AmitBL
Jul 30 at 10:33















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