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Nonplanarity of unit
graphs and classification of the toroidal ones
A. K. Das, H. R. Maimani, M. R. Pournaki and S. Yassemi |
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Vol. 268 (2014), No. 2, 371–387
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Abstract |
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The unit graph of a ring with nonzero identity is the graph in which the vertex set is , and two distinct vertices and are adjacent if and only if is a unit in . 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, unit graph, genus
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Mathematical Subject Classification 2010
Primary: 05C75
Secondary: 13M05
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Milestones
Received: 27 July 2012
Revised: 8 July 2013
Accepted: 12 July 2013
Published: 21 June 2014
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Authors |
| A. K. Das | |
| Department of Mathematics North-Eastern Hill University Permanent Campus Shillong-793022 Meghalaya India |
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| H. R. Maimani | |
| Mathematics Section Department of Basic Sciences Shahid Rajaee Teacher Training University P.O. Box 16785-163 |
School of Mathematics Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5746 Tehran Iran |
| M. R. Pournaki | |
| Department of Mathematical
Sciences Sharif University of Technology P.O. Box 11155-9415 |
School of Mathematics Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5746 Tehran Iran |
| S. Yassemi | |
| School of Mathematics, Statistics
and Computer Science College of Science University of Tehran |
School of Mathematics Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5746 Tehran Iran |
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