Abstract In this paper, we introduce a graph structure, called the single non-zero component graph Γ (V) (V), on a finite dimensional vector space V V. We study the minimal domination sets as well as minimum independent domination sets, and compute the domination number of Γ (V) (V). Furthermore, using the domination number and minimum independent domination sets, respectively, we prove that two vector spaces are isomorphic if and only if the corresponding single nonzero component graphs are isomorphic, and determine the automorphisms of Γ (V) (V). Finally, we characterize the maximum independent sets when the dimension of V V is not more than 5.
Xi et al. (Thu,) studied this question.