Sharma, P. K. ; Bhatwadekar, S. M.
(1995)
*A note on graphical representation of rings*
Journal of Algebra, 176
(1).
pp. 124-127.
ISSN 0021-8693

Full text not available from this repository.

Official URL: http://dx.doi.org//10.1006/jabr.1995.1236

Related URL: http://dx.doi.org/10.1006/jabr.1995.1236

## Abstract

Let R be a commutative ring with identity. Let G be a graph with vertices as elements of R, where two distinct vertices x and y are adjacent if and only if Rx + Ry = R. In this paper we show that a commutative ring R is a finite ring if and only if the graph G (associated with R as above) is finitely colourable. Moreover we show that in this case the chromatic number of the graph G is the sum of the number of maximal ideals and the number of units of R.

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

ID Code: | 3214 |

Deposited On: | 11 Oct 2010 09:58 |

Last Modified: | 18 May 2011 10:23 |

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