Component graphs of vector spaces and zero-divisor graphs of ordered sets

In this paper, nonzero component graphs and nonzero component union graphs of finite-dimensional vector spaces are studied using the zero-divisor graph of a specially constructed 0–1-distributive lattice and the zero-divisor graph of rings. Furthermore, we define an equivalence relation on nonzero component graphs and nonzero component union graphs to deduce that these graphs are the graph join of zero-divisor graphs of Boolean algebras and complete graphs. The last section characterizes the perfect and chordal nonzero component and nonzero component union graphs. Additionally, we observe that the nonzero component graph and reduced nonzero component union graph of free semi-modules could be treated as the zero-divisor graph of a 0–1-distributive lattice.