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Necessary and
sufficient conditions for unit graphs to be Hamiltonian
H. R. Maimani, M. R. Pournaki and S. Yassemi |
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Vol. 249 (2011), No. 2, 419–429
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Abstract |
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The unit graph corresponding to an associative ring R is the graph obtained by setting all the elements of R to be the vertices and defining distinct vertices x and y to be adjacent if and only if x + y is a unit of R. By a constructive method, we derive necessary and sufficient conditions for unit graphs to be Hamiltonian. |
Keywords
Hamiltonian cycle, Hamiltonian graph, finite ring
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Mathematical Subject Classification 2000
Primary: 05C45
Secondary: 13M05
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Milestones
Received: 28 December 2009
Revised: 14 July 2010
Accepted: 31 July 2010
Published: 1 February 2011
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Authors |
| H. R. Maimani | |
| Mathematics Section, Department of
Basic Sciences Shahid Rajaee Teacher Training University P.O. Box 16785-163 Tehran Iran |
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 Tehran Iran |
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| http://math.ipm.ac.ir/pournaki/ | |
| S. Yassemi | |
| School of Mathematics, Statistics
and Computer Science College of Science University of Tehran Tehran Iran |
School of Mathematics Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5746 Tehran Iran |
| http://math.ipm.ac.ir/yassemi/ | |
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