Algorithms to Determine the Distance-t Dominating Sets of ES(n, k)

The distance- t dominating set is an interesting property used in the allocation of finite resources to a massively parallel architecture. The distance -t dominating set also helps in sharing resources amongst the nodes and thereby lays the framework for designing alternate parallel paths should one or more of the nodes fail. In this paper we discuss the process of determining the distance-t- dominating set of the extended star graph ES(n, k.). We design the algorithms to determine the distance-t dominating sets of ES for lower integers such as t = 2, 3, 4, 5 and then using the above mentioned algorithms we design generalized algorithms to determine the distance-t dominating set of ES for all t where t> 2.