In a computer network there are two types of nodes: client and server. Each client is directly connected (using network cables) to at least one server and there are no direct connections between clients. Suppose that each server can route messages to other servers with which it is directly connected and the entire network is connected(the set of servers is connected). In order to make the network more reliable, one scenario is considered:
- Every client is directly connected to at least 2 servers and every pair of servers having the distance between them 2 are connected using a direct cable. Prove that, in this new network, if a server becomes unavailable the clients can still communicate with all the remaining servers.
I realised that there are at least two paths which connect a client with a server, but I don't know how to prove that if a server becomes unavailable the clients can still communicate with all the remaining servers.