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Prime Graph of Cartesian Product of Rings
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 69 - Number 10 |
| Year of Publication: 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
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
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