2-Shortest and Strong Shortest Path Union Cover for Networks

Interconnection networks play a key role in the design and implementation of communicationnetworks and the recent advent of optic technology add more design problems. In general, aninterconnection network may be modeled by a simple graph whose nodes represent components ofthe network and whose links represent physical communication links. Let be a graph. Strong shortest path union cover is defined as for all (G), there exists such that lies on unique fixed shortest path where. Strong Shortest path Union covering number of a graph is the minimum cardinality among all strong shortest path union cover of and it is denoted by. The strong shortest path cover problem is to cover every edge of a known graph representing a network by the strong unique shortest paths from a subset of vertices in the graph.In this paper, we determinethe -shortest path and strong shortest path union cover for Enhancedhypercube network  Augumented hypercube networkCrossed cube network.