Algorithms to compute some dominating sets of ES (n, k) and ESC (n, k)

Dominating sets are used in the allocation of finite resources to massively parallel architectures. In this paper, we propose a new way of determining a minimal dominating set, connected dominating set and total dominating set of an extended star graph ES (n, k) as well as the extended star graph with cross-connections ESC (n, k) using the levels of its architecture instead of nodes thereby reducing the running time of a domination algorithm significantly.