TY - JOUR
ID - 2843
TI - NON-NILPOTENT GRAPH OF COMMUTATIVE RINGS
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Hoque, Hussain Mohammed Imdadul
AU - Saikia, Helen Kumari
AU - Goswami, Jituparna
AU - Patwari, Diksha
AD - Department of Mathematics, Gauhati University, Guwahati-781014, India.
AD - Department of Mathematics, Gauhati University, Guwahati-14, Assam, India.
Y1 - 2024
PY - 2024
VL - 12
IS - 1
SP - 149
EP - 162
KW - Commutative rings
KW - Non-nilpotent graph
KW - Nilpotent elements, Non-nilpotent elements
DO - 10.22044/jas.2023.12064.1620
N2 - Let R be a commutative ring with unity. Let Nil(R) be the set of all nilpotent elements of R and Nil(R) = R \ Nil(R) be the set of all non-nilpotent elements of R. The non-nilpotent graph of R is a simple undirected graph GNN(R) with Nil(R) as vertex set and any two distinct vertices x and y are adjacent if and only if x+y ∈ Nil(R).In this paper, we introduce and discuss the basic properties of the graph GNN(R). We also study the diameter and girth of GNN(R). Further, we determine the domination number and the bondage number of GNN(R). We establish a relation between diameter and domination number of GNN(R). We also establish a relation between girth and bondage number of GNN(R).
UR - https://jas.shahroodut.ac.ir/article_2843.html
L1 - https://jas.shahroodut.ac.ir/article_2843_3c09101e97af59b1db3801b6537792ce.pdf
ER -