2-Shortest and Strong Shortest Path Union Cover for Networks


Santiagu Theresal
Department of Mathematics, Auxilium College of Arts and Science for Women
S. Arul Amirtha Raja
Department of Mathematics, St. Joseph’s College of Engineering, OMR, Chennai-600 119


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.

October 19, 2023