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 $A_{G_1 \otimes G_2}$
- 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 : $\omega(G_1 \otimes G_2) = \max\{\omega(G_1),\omega(G_2)\}$
I'm preety clueless about this subject so you can be extra informative on how to solve it, I'll be grateful. Thank you!.