Dwi Mifta Mahanani, Dewi Ismiarti, Syaiful Anam
Let R be a commutative ring and M be an R-module. In this paper, we define minimal submodules graph of M, denoted by Γmin(M), in which the vertex set is the set of nonzero proper submodules of M. Two distinct vertices A and B are adjacent provided that A ∩ B is a minimal submodule of M. In this study, we associate some properties of the graph from the properties of module and vice versa. Moreover, if we have an R-module homomorphism from M to M′, we compare some invariant numbers and properties of Γmin(M) and Γmin(M′). © 2026, Hacettepe University. All rights reserved.
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Brawijaya University, East Java, 65145, Indonesia; Department of Mathematics, Universitas Islam Negeri Maulana Malik Ibrahim, East Java, 65145, Indonesia
