Vol. 249, No. 2, 2011

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Necessary and sufficient conditions for unit graphs to be Hamiltonian

H. R. Maimani, M. R. Pournaki and S. Yassemi

Vol. 249 (2011), No. 2, 419–429
Abstract

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
Mathematical Subject Classification 2000
Primary: 05C45
Secondary: 13M05
Milestones
Received: 28 December 2009
Revised: 14 July 2010
Accepted: 31 July 2010
Published: 1 February 2011
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
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/