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

Abstract

In this paper, nonzero component graphs and nonzero component union graphs of finite dimensional vector space are studied using the zero-divisor graph of specially constructed 0-1-distributive lattice and the zero-divisor graph of rings. Further, 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. In the last section, we characterize the perfect and chordal nonzero component graphs and nonzero component union graphs.