On the SD number and the ID number of generalized hypercube networks

Generalized hypercube is an interconnection network topology that exhibits excellent performance and symmetry; it facilitates the expansion of capacity and the upgrading of resources to accommodate larger demands; the domination parameters serve as a crucial foundation for the analysis and quantification of the dependability of interconnection networks. In this paper, we explore the structure and properties of generalized hypercube networks to establish the bounds of signed domination numbers and Italian domination numbers. We also present a vertex set partitioning approach to investigate these parameters for some small dimensional generalized hypercube networks and hypercube networks. Furthermore, a Vizing-type conjecture was proposed that satisfies the signed domination number and Italian domination number of generalized hypercube networks.