The wiener index of the zero-divisor graph for a new class of residue class rings
The zero-divisor graph of a commutative ring R, denoted by Γ( R ), is a graph whose two distinct vertices x and y are joined by an edge if and only if xy = 0 or yx = 0. The main problem of the study of graphs defined on algebraic structure is to recognize finite rings through the properties of vario...
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| Published in | Frontiers in chemistry Vol. 10; p. 985001 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Frontiers Media S.A
13.09.2022
|
| Subjects | |
| Online Access | Get full text |
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| Summary: | The zero-divisor graph of a commutative ring R, denoted by Γ(
R
), is a graph whose two distinct vertices
x
and
y
are joined by an edge if and only if
xy
= 0 or
yx
= 0. The main problem of the study of graphs defined on algebraic structure is to recognize finite rings through the properties of various graphs defined on it. The main objective of this article is to study the Wiener index of zero-divisor graph and compressed zero-divisor graph of the ring of integer modulo
p
s
q
t
for all distinct primes
p
,
q
and
s
,
t
∈
N
. We study the structure of these graphs by dividing the vertex set. Furthermore, a formula for the Wiener index of zero-divisor graph of Γ(
R
), and a formula for the Wiener index of associated compressed zero-divisor graph Γ
E
(
R
) are derived for
R
=
Z
p
s
q
t
. |
|---|---|
| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 Reviewed by: Hongjie Bi, Okinawa Institute of Science and Technology Graduate University, Japan Wei Wang, Chongqing Medical University, China Edited by: Xiyun Zhang, Jinan University, China This article was submitted to Theoretical and Computational Chemistry, a section of the journal Frontiers in Chemistry |
| ISSN: | 2296-2646 2296-2646 |
| DOI: | 10.3389/fchem.2022.985001 |