Suppose each server is connected to exactly d other server, and there are

n servers total. Now a single server is infected with a malware, and the malware is

spreading across the network.$($a$)$ Suppose there are currently k servers that are infected by the malware.

Give an upper bound on the number edges that need to be cut to contain the

malware using the second eigenvalue of the adjacency matrix.$($b$)$On the other hand suppose there are two groups, each with k$/2$ servers,

such that are connected only by a single edge. Give an upper bound on the second

eigenvalue of the adjacency matrix. $($Hint: look at the Laplacian matrix$)$