What protocol can a vEdge router run to establish connectivity within the local area network (LAN)?

The correct choice is OSPF (Open Shortest Path First), which is a widely used interior gateway protocol. OSPF is designed for IP networks and operates within a single autonomous system, making it suitable for establishing connectivity in local area networks (LANs).

OSPF uses a link-state routing algorithm to maintain a database of the entire network's topology, allowing routers to make routing decisions based on the shortest path to any given destination. This protocol is particularly effective in larger networks where scalability and fast convergence are essential. OSPF also supports advanced features such as area hierarchies, which can help manage routing overhead and improve efficiency within the LAN environment.

In scenarios involving vEdge routers, utilizing OSPF can enhance network performance by enabling efficient routing updates and allowing for dynamic adaptation to changes in the network topology.