Analysis of Adjacency, Laplacian and Distance Matrices of Zero Divisor Graphs of 4-Radical Zero Completely Primary Finite Rings

Abstract

This study is an extension of our study on matrices of zero divisor graphs of classes of 3-radical zero completely primary finite rings. It focusses on Matrices of a class of finite rings R whose subset of the zero divisors Z(R) satisfies the condition (Z(R))4 = (0) and (Z(R))3 ̸= (0) for all characteristics of R that is; p, p2 , p3 and p 4 . We have formulated the zero divisor graphs Γ(R) of R and associated them with three classes of matrices, namely, the Adjacency matrix [A], the Laplacian matrix [L] and the Distance matrix [dij ]. The study has further characterized the properties of the graphs Γ(R) and the matrices mentioned.