A note on graphical representation of rings

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


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
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

Repository Staff Only: item control page