Research Article
Prime Graph of Cartesian Product of Rings
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
|
| Volume 69 - Issue 10 |
| Published: May 2013 |
| Authors: Sanjoy Kalita, Kuntala Patra |
10.5120/11877-7681
|
Sanjoy Kalita, Kuntala Patra . Prime Graph of Cartesian Product of Rings. International Journal of Computer Applications. 69, 10 (May 2013), 13-16. DOI=10.5120/11877-7681
@article{ 10.5120/11877-7681,
author = { Sanjoy Kalita,Kuntala Patra },
title = { Prime Graph of Cartesian Product of Rings },
journal = { International Journal of Computer Applications },
year = { 2013 },
volume = { 69 },
number = { 10 },
pages = { 13-16 },
doi = { 10.5120/11877-7681 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2013
%A Sanjoy Kalita
%A Kuntala Patra
%T Prime Graph of Cartesian Product of Rings%T
%J International Journal of Computer Applications
%V 69
%N 10
%P 13-16
%R 10.5120/11877-7681
%I Foundation of Computer Science (FCS), NY, USA
Abstract
Let R be a commutative ring. The prime graph of the ring R is defined as a graph whose vertex set consists of all elements of R and any two distinct vertices x and y are adjacent if and only if xRy=0 or yRx=0. This graph is denoted by PG(R). In this paper we investigate some relations between the chromatic number of prime graph of finite product of commutative rings and the chromatic number of prime graph of these rings. We also obtain some results on the chromatic number of prime graph of the ring Z_m×Z_n.
References
- D. F. Anderson and P. S. Livingston, The Zero-divisor graph of a commutative ring, J. Algebra 217 (1999), no. 2, 434–447.
- I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), no. 1, 208–226.
- S. Bhavanari , S. P. Kuncham and N. Dasaari, Prime Graph of a Ring, J. of Combinatorics, Information and System Sources, vol 35 (2010) No 1-2, 27-42.
- F. Harary, Graph Theory, Eddison Wesley Publishing Company inc. 1969.
- J. Lambek, Lectures on Rings and Modules, Blaisdel Publ. Co. 1966.
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