Title : ( The matrix Jacobson graph of finite commutative rings )
Authors: Siti Humaira , Pudji Astuti , Intan Muchtadi-Alamsyah , Ahmad Erfanian ,
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Abstract
The matrix Jacobson graph was introduced in 2019 as a generalization of Jacobson graph and narray Jacobson graph. Let R be a commutative ring and J(R) be the Jacobson radical of the ring R. The matrix Jacobson graph of the ring R of size m × n, denoted by J(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 the ring R. Here we obtain some graph theoretical properties of J(R)m×n including its connectivity, planarity and perfectness.
Keywords
, finite commutative rings, matrix Jacobson graph, connectivity, planarity, perfectness
@article{paperid:1094263,
author = {Siti Humaira and Pudji Astuti and Intan Muchtadi-Alamsyah and Erfanian, Ahmad},
title = {The matrix Jacobson graph of finite commutative rings},
journal = {Electronic Journal of Graph Theory and Applications},
year = {2022},
volume = {10},
number = {1},
month = {March},
issn = {2338-2287},
pages = {181--197},
numpages = {16},
keywords = {finite commutative rings; matrix Jacobson graph; connectivity; planarity; perfectness},
}
%0 Journal Article
%T The matrix Jacobson graph of finite commutative rings
%A Siti Humaira
%A Pudji Astuti
%A Intan Muchtadi-Alamsyah
%A Erfanian, Ahmad
%J Electronic Journal of Graph Theory and Applications
%@ 2338-2287
%D 2022
