Network Topology

Correct Answer: Partial mesh topology

The most appropriate topology for a small expandable business network that requires fault tolerance is the Partial Mesh topology. In this topology, not all devices are directly connected to every other, but there are multiple paths to move data from one device to another, which increases fault tolerance by providing alternative paths in case one path fails. The partial mesh topology also allows easy scalability as new devices can be added without disrupting the network. On the other hand, the Star topology does not provide as much fault tolerance because if the central node fails, the entire network comes down. The Bus topology also lacks fault tolerance and is not expandable as adding new devices can disrupt the network. Finally, the Ring topology, while offering some fault tolerance, is not easily expandable or adaptable to network changes.

Correct Answer: Star topology

A network administrator that needs to establish a network topology that is both easy to troubleshoot and cost-effective should choose a Star topology. A Star topology uses a central hub or switch where all nodes are connected independently. This topology is ideal in terms of troubleshooting because the failure of one node does not affect the others, unlike in a ring or bus topology. Also, it's cost-effective because it requires less cabling than a Mesh topology. A Mesh topology, although robust and reliable, has a high setup cost due to the full interconnection of nodes. A Bus topology, while cost-effective, can be challenging to manage and troubleshoot because all nodes share the same communication line. Lastly, a Ring topology can be difficult to troubleshoot and can entirely fail if one node in the ring fails.

Correct Answer: Fully mesh topology

The correct topology in this case would be the Fully Mesh Topology. This is due to the fact that it creates multiple redundant paths between devices, thereby reducing the chances of network failure and providing a high level of redundancy. In contrast, the Star topology, Bus topology, and Ring topology do not inherently offer multiple redundant paths. Thus, if a single point of failure occurs in Star, Bus, or Ring topologies, it could potentially disrupt the entire network. As such, while these other topologies may be suitable in certain scenarios, for the requirement of redundancy and resilience against network failures, Fully Mesh topology is the best answer.