The intersection graph Gz(Zn) of zero divisors of the ring Zn is a simple undirected graph whose vertices are the non-zero zero divisors of Zn and two distinct vertices x and y are adjacent if and only if their corresponding principal ideals having a non-zero intersection in Zn. We obtain the vertex independence number and edge independence number of the graph Gz(Zn) for all characterizations of n. Also, we find the vertex covering number and edge covering number of the graph Gz(Zn) for all values of n.

1.
M. B.
Nathanson
,
Elementary Methods in Number theory
, (
Springer
,
India
,
2005
).
2.
D. F.
Anderson
and
P. S.
Livingston
,
The zero-divisor graph of a commutative ring
, (
Journal of Algebra
,
217
,
1999
), pp.
434
447
.
3.
I.
Beck
,
Coloring of commutative rings
, (
Journal of Algebra
,
116
,
1988
), pp.
208
226
.
4.
J. A.
Bondy
and
U. S. R.
Murthy
,
Graph theory with Applications
, (
Macmillan Press Ltd
.,
Great British
,
1976
).
5.
E. A.
Osba
,
S.
Al-Addasi
and
A.
Omar
,
Some properties of the intersection graph for finite commutative principal ideal ring
, (
International Journal of Combinatorics, Hindawi Publishing Corporation
,
2014
), pp.
1
6
.
6.
S.
Sajana
,
K. K.
Srimitra
and
D.
Bharathi
,
Intersection Graph of Zero divisors of a finite commutative ring
, (
International Journal of Pure and Applied Mathematics
, Vol.
109
(
7
),
2017
), pp.
51
58
.
7.
S.
Sajana
and
D.
Bharathi
,
Number theoretic properties of the commutative ring Zn
, (
International Journal of Research in Industrial Engineering
, Vol.
8
(
1
),
2019
), pp.
77
88
.
8.
S.
Sajana
and
D.
Bharathi
,
Hamiltonian property of intersection graph of zero divisors of the ring Zn
, (
Malaya Journal of Matematik
, Vol.
6
(
1
),
2018
), pp.
133
139
.
9.
M. B.
Nathanson
,
Connected components of arithmetic graphs
, (
Monatshefte fur Mathematik
,
89
,
1980
), pp.
219
222
.
This content is only available via PDF.
You do not currently have access to this content.