Abstract
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.
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