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Nonplanarity of unit graphs and classification of the toroidal ones
Das, A. K ; Sharif University of Technology
244
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- Type of Document: Article
- DOI: 10.2140/pjm.2014.268.371
- Abstract:
- The unit graph of a ring R with nonzero identity is the graph in which the vertex set is R, and two distinct vertices x and y are adjacent if and only if x + y is a unit in R. In this paper, we derive several necessary conditions for the nonplanarity of the unit graphs of finite commutative rings with nonzero identity, and determine, up to isomorphism, all finite commutative rings with nonzero identity whose unit graphs are toroidal
- Keywords:
- Finite commutative ring ; Genus ; Unit graph
- Source: Pacific Journal of Mathematics ; Vol. 268, Issue. 2 , 2014 , pp. 371-387 ; ISSN: 0030-8730
- URL: http://msp.org/pjm/2014/268-2/p06.xhtml