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Rainbow Connection Number in Pyramid Networks

Published: 16 January 2019 Publication History

Abstract

Rainbow connection number of a connected graph G is the minimum number of colors needed to color the edges of G, so that every pair of vertices is connected by at least one path whose edges have distinct colors. In this paper, we propose a linear time algorithm for constructing a rainbow coloring on pyramids.

References

[1]
Ahadi, A., Dehghan, A.: On Rainbow Connection of Strongly Regular Graphs. Arxiv preprint arXiv:1001.3413v1 {math.CO} (2010)
[2]
Basavaraju, M., Chandran, L.S., Rajendraprasad, D., Ramaswamy, A.: Rainbow Connection Number and Radius. Arxiv preprint arXiv:1011.0620v1 {math.CO} (2010)
[3]
Caro, Y., Lev, A., Roditty, Y., Tuza, Z., Yuster, R.: On Rainbow Connection. The Electronic Journal of Combinatorics 15, #R57 (2008)
[4]
Chakraborty, S., Fischer, E., Matsliah, A., Yuster, R.: Hardness and Algorithms for Rainbow Connection. Journal of Combinatorial Optimization 21(3), 330--347 (2011)
[5]
Chartrand, G., Johns, G.L., McKeon, K.A., Zhang, P.: Rainbow Connection in Graphs. Mathematica Bohemica 133(1), 85--98 (2008)
[6]
Culler, D.E., Singh, J.P., Gupta, A.: Parallel Computer Architecture: A Hardware/Software Approach, Morgan Kaufmann, San Francisco, CA, 1999
[7]
Ericksen, A.: A Matter of Security. Graduating Engineer & Computer Careers, 24--28 (2007)
[8]
Hsieh, H.J., Duh, D.R.: ω-wide diameters of enhanced pyramid networks, Theoretical Computer Science 412(29), 3658--3675 (2011)
[9]
Krivelevich, M., Yuster, R.: The Rainbow Connection of a Graph is (at most) Reciprocal to Its Minimum Degree, Journal of Graph Theory 63(3), 185--191 (2009)
[10]
Li, X., Shi, Y.: Rainbow Connection in 3-connected Graphs. Arxiv preprint arXiv:1010.6131v1 {math.CO} (2010)
[11]
Li, X., Sun, Y.: Rainbow Connection of Graphs- A Survay, arXiv:1101.5747v1 {math.CO} (2011)
[12]
Li, X., Sun, Y.: Rainbow connection of graphsA survey, Graphs and Combinatorics 29(1), 1--38 (2013)
[13]
Miller, R., Stout, Q.F.: Simulating essential pyramids, IEEE Transactions on Computers 37(12), 16421648 (1988)
[14]
Stout, Q.F.: Pyramid computer solutions of the closest pair problem, Journal of Algorithms 6, 200--212 (1985)
[15]
Shahhoseini, H.S., Kandzi, E.S., Mollajafari, M.: Nonflat surface level pyramid: a high connectivity multidimensional interconnection network, The Journal of Supercomputing 67(1) 31--46 (2014)
[16]
Wang, F.H., Sung, G.S.: Rainbow Connection Number in Triangular Pyramids. In: 29th Workshop on Combinatorial Mathematics and Computation Theory. Taipei, Taiwan 2012

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ICCMS '19: Proceedings of the 11th International Conference on Computer Modeling and Simulation
January 2019
253 pages
ISBN:9781450366199
DOI:10.1145/3307363
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

In-Cooperation

  • University of Wollongong, Australia
  • College of Technology Management, National Tsing Hua University, Taiwan
  • Swinburne University of Technology
  • University of Technology Sydney

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 16 January 2019

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Author Tags

  1. Pyramid networks
  2. Rainbow coloring
  3. Rainbow connection number
  4. Rainbow path

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  • Research-article
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  • Refereed limited

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ICCMS 2019
ICCMS 2019: The 11th International Conference on Computer Modeling and Simulation
January 16 - 19, 2019
QLD, North Rockhampton, Australia

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