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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Siti Humaira
Bandung Institute of Technology
Electrical & Electronics Engineering

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The matrix Jacobson graph of finite commutative rings Siti Humaira; Pudji Astuti; Intan Muchtadi-Alamsyah; Ahmad Erfanian
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2022.10.1.12

Abstract

The notion of the matrix Jacobson graph was introduced in 2019. Let R be a commutative ring and J(R) be the Jacobson radical of ring R. The matrix Jacobson graph of ring R size m × n, denoted ????(R)m × n, is defined as a graph where the vertex set is Rm × n ∖ J(R)m × n such that two distinct vertices A, B are adjacent if and only if 1 − det(AtB) is not a unit in ring R. Here we obtain some graph theoretical properties of ????(R)m × n including its connectivity, planarity and perfectness.
Co-Authors Ahmad Erfanian Intan Muchtadi-Alamsyah Pudji Astuti