45
Views
4
CrossRef citations to date
0
Altmetric
Section A

Length two path-centred surface areas for the arrangement graph

, &
Pages 1170-1189 | Received 09 Feb 2013, Accepted 19 Jul 2013, Published online: 24 Sep 2013

References

  • S. B. Akers, B. Krishnamurthy, A group theoretic model for symmetric interconnection networks, IEEE Trans. Comput. 38 (1989), pp. 555–566 doi: 10.1109/12.21148
  • M. Bae, B. Bose, Resource placement in torus-based networks, IEEE Trans. Comput. 46 (1997), pp. 1083–1092 doi: 10.1109/12.628393
  • E. Cheng, K. Qiu, Z. Shen, On deriving explicit formulas of the surface areas for the arrangement graphs and some of the related graphs, Int. J. Comput. Math. 87 (2010), pp. 2903–2914
  • E. Cheng, K. Qiu, Z. Shen, Length two path centered surface area for bipartite graphs, preprint, J. Combin. Math. Combin. Comput. 2012 to appear in
  • E. Cheng, L. Lipták, K. Qiu, Z. Shen, On deriving conditional diagnosability of interconnection networks, Inform. Process. Lett. 112 (2012), pp. 674–677 doi: 10.1016/j.ipl.2012.06.008
  • K. Day, A. Tripathi, Arrangement graphs: A class of generalized star graphs, Inform. Process. Lett. 42 (1992), pp. 235–241 doi: 10.1016/0020-0190(92)90030-Y
  • G. Fertin, A. Raspaud, k-Neighbourhood broadcasting, Proceedings of the 8th International Colloquium on Structural Information and Communication Complexity (SIROCCO’01), CataloniaSpain, 2001, pp. 133–146
  • N. Imani, H. Sarbazi-Azad, S. G. Akl, Some combinatorial properties of the star graphs: The surface area and volume, Discrete Math. 309 (2009), pp. 560–569 doi: 10.1016/j.disc.2008.08.007
  • J. S. Jwo, S. Lakshmivarahan, S. K. Dhall, A new class of interconnection networks based on the alternating graph, Networks 23 (1993), pp. 315–326 doi: 10.1002/net.3230230414
  • P.-L. Lai, J. J.M. Tan, C.-P. Chang, L.-H. Hsu, Conditional diagnosability measures for large multiprocessor systems, IEEE Trans. Comput. 54 (2005), pp. 165–175 doi: 10.1109/TC.2005.19
  • C. K. Lin, J. M. Tan, L. H. Hsu, E. Cheng, L. Lipták, Conditional diagnosability of Cayley graphs generated by transposition trees under the comparison diagnosis model, J. Interconnection Netw. 9 (2008), pp. 83–97 doi: 10.1142/S0219265908002175
  • J. Maeng, M. Malek, A comparison connection assignment for self-diagnosis of multiprocessor systems, Proceedings of the 11th International Symposium on Fault-Tolerant Computing, Portland, ME, 1981, pp. 173–175
  • M. Malek, A comparison connection assignment for diagnosis of multiprocessor systems, Proceedings of the 7th International Symposium on Computer Architecture, La BauleFrance, 1980, pp. 31–35
  • F. Portier, T. Vaughan, Whitney numbers of the second kind for the star poset, Eur. J. Combinator. 11 (1990), pp. 277–288 doi: 10.1016/S0195-6698(13)80127-8
  • J. Riordan, An Introduction to Combinatorial Analysis, Wiley, New York, 1980
  • M. Sampels, Vertex-symmetric generalized Moore graphs, Discrete Appl. Math. 138 (2004), pp. 195–202 doi: 10.1016/S0166-218X(03)00294-4
  • H. Sarbazi-Azad, M. Ould-Khaoua, L. Mackenzie, S. G. Akl, On the combinatorial properties of k-ary n-cubes, J. Interconnection Netw. 5 (2004), pp. 79–91 doi: 10.1142/S0219265904001039
  • I. Stewart, A general technique to establish the asymptotic conditional diagnosability of interconnection networks, Theoret. Comput. Sci. 452 (2012), pp. 132–137 doi: 10.1016/j.tcs.2012.05.015
  • L. Wang, S. Subrammanian, S. Latifi, P. K. Srimani, Distance distribution of nodes in star graphs, Appl. Math. Lett. 19 (2006), pp. 780–784 doi: 10.1016/j.aml.2005.09.004

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.