ABSTRACT
Networks are typically built in the real world by connecting smaller networks together to form larger ones. For example, two or more individual machines connected on a hub or a switch form a PAN (Personal Area Network). A CAN (Campus Area Network) connects two or more LANs (Local Area Networks) and is limited to a specific and contiguous geographical area such as a college campus, industrial complex, or a military base. A MAN (Metropolitan Area Network) connects two or more LANs or CANs together and is limited to the geographical bounds of a city. An internetwork is created by connecting two or more networks or network segments using routers, and so on. These examples of “natural” network growth suggest modeling networks as combinations of graphs. Some graph combinations—binary operations—that appear in the literature are defined below. The discussion focuses on the diameter and vulnerability of network combinations.
