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Let  G = BH n be a  n  - dimensional balanced hypercube. As a topology of interconnection network, balanced hypercubes are widely used in many areas. The signed  k  - subdomination number of graphs is an important parameter in the domination theory. In this paper, according to the properties of balanced hypercubes, the signed (| G | –1) - subdomination number of balanced hypercubes when  n  = 2 is determined by classified discussion and exhaustived method.

The signed (|G| –1)-subdomination number of balanced hypercubes