Home Articles List Article Information
Transactions on Combinatorics
Journal Archive
Volume Volume 8 (2019)
Volume Volume 7 (2018)
Volume Volume 6 (2017)
Volume Volume 5 (2016)
Volume Volume 4 (2015)
Volume Volume 3 (2014)
Volume Volume 2 (2013)
Volume Volume 1 (2012)
Hoshur, R., Vumar, E. (2012). Hamilton-connected properties in cartesian product. Transactions on Combinatorics, 1(3), 11-19. doi: 10.22108/toc.2012.1871
Rushengul Hoshur; Elkin Vumar. "Hamilton-connected properties in cartesian product". Transactions on Combinatorics, 1, 3, 2012, 11-19. doi: 10.22108/toc.2012.1871
Hoshur, R., Vumar, E. (2012). 'Hamilton-connected properties in cartesian product', Transactions on Combinatorics, 1(3), pp. 11-19. doi: 10.22108/toc.2012.1871
Hoshur, R., Vumar, E. Hamilton-connected properties in cartesian product. Transactions on Combinatorics, 2012; 1(3): 11-19. doi: 10.22108/toc.2012.1871

Hamilton-connected properties in cartesian product

Article 3, Volume 1, Issue 3, September 2012, Page 11-19  XML PDF (445 K)
Document Type: Research Paper
DOI: 10.22108/toc.2012.1871
Authors
Rushengul Hoshur; Elkin Vumar
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
Abstract
In this paper‎, ‎we investigate a problem of finding natural condition‎ ‎to assure the product of two graphs to be hamilton-connected‎. ‎We present some‎ ‎sufficient and necessary conditions for $G\Box H$ being hamilton-connected when $G$ is a‎ ‎hamilton-connected graph and $H$ is a tree or $G$ is a hamiltonian‎ ‎graph and $H$ is $K_2$‎.
Keywords
Cartesian product; Hamilton-connectedness; Hamilton cycle; Hamilton path
Main Subjects
05C38 Paths and cycles; 05C45 Eulerian and Hamiltonian graphs
References
J. A. Bondy and U. S. R. Murty (1976). Graph Theory with Applications. Macmillan, New York.
W. S. Chiue and B. S. Shieh (1999). On connectivity of the Cartesian product of two graphs. Appl. Math. Comput.. 102, 129-137
E. Flandrin, H. Li and R. Cada (2006). Hamiltonicity and pancyclicity of generalaized prisms. Discrete Math.. 24, 61-67
R. Gould (2003). Advances on the Hamiltonian Problem -A Survey. Graphs and Combinatorics. 19, 7-52
W. Goddard and M. A. Henning (2001). Pancyclicity of the prism. Discrete Math.. 234, 139-142
P. R. Goodey and M. Rosenfeld (1978). Hamiltonian circuits in prisms over certain simple 3-polytopes. Discrete Math.. 21, 229-235
L.-H. Hsu and C.-K. Lin (2008). Graph Theory and Interconnection Networks. CRC press.
T. Kaiser, Z. Ryj'{a}v{c}ek, D. Kral, M. Rosenfeld and H. J. Voss (2007). Hamilton Cycle in Prisms. J. Graph Theory. 56, 249-269
M. Lu, H-J. Lai and H. Li (2009). Hamiltonian properties in Cartesian product. Manuscript.
K. Ozeki (2009). A degree sum condition for graphs to be prisim Hamiltonian. Discrete Math.. 309, 4266-4299
P. Paulraja (1993). A characterization of hamiltonian prisms. J. Graph Theory. 17, 161-171
M. Rosenfeld and D. Barnette (1973). Hamiltonian circuits in certain prisms. Discrete Math.. 5, 389-394
Statistics
Article View: 4,056
PDF Download: 3,477