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An Upper Bound of the Rainbow Connection Number in RTCC Pyramids

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Book cover Advances in Intelligent Systems and Applications - Volume 1

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 20))

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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 an upper bound to the size of the rainbow connection number in Recursive Transpose-Connected 4-Cycles (RTCC) pyramids.

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References

  1. Ahadi, A., Dehghan, A.: On Rainbow Connection of Strongly Regular Graphs. Arxiv preprint arXiv:1001.3413v1 [math.CO] (2010)

    Google Scholar 

  2. Basavaraju, M., Chandran, L.S., Rajendraprasad, D., Ramaswamy, A.: Rainbow Connection Number and Radius. Arxiv preprint arXiv:1011.0620v1 [math.CO] (2010)

    Google Scholar 

  3. Caro, Y., Lev, A., Roditty, Y., Tuza, Z., Yuster, R.: On Rainbow Connection. The Electronic Journal of Combinatorics 15, #R57 (2008)

    MathSciNet  Google Scholar 

  4. Chakraborty, S., Fischer, E., Matsliah, A., Yuster, R.: Hardness and Algorithms for Rainbow Connection. Journal of Combinatorial Optimization 21(3), 330–347 (2011)

    Article  MathSciNet  Google Scholar 

  5. Chartrand, G., Johns, G.L., McKeon, K.A., Zhang, P.: Rainbow Connection in Graphs. Mathematica Bohemica 133(1), 85–98 (2008)

    MathSciNet  MATH  Google Scholar 

  6. Ericksen, A.: A Matter of Security. Graduating Engineer & Computer Careers, 24–28 (2007)

    Google Scholar 

  7. Kourdy, R., Rad, M.R.N.: RTCC-Pyramid-NOC: Scalable, Regular and Symmetric Network-on-chip Topology. The Journal of Computing 4, 58–64 (2012)

    Google Scholar 

  8. 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)

    MathSciNet  Google Scholar 

  9. Li, X., Shi, Y.: Rainbow Connection in 3-connected Graphs. Arxiv preprint arXiv:1010.6131v1 [math.CO] (2010)

    Google Scholar 

  10. Li, X., Sun, Y.: Rainbow Connection of Graphs–A Survay, arXiv:1101.5747v1 [math.CO] (2011)

    Google Scholar 

  11. Razavi, S., Sarbazi-Azad, H.: The RTCC Pyramid: Routing and Topological Properties. Information Sciences 180, 2328–2339 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wang, F.H., Sung, G.S.: Rainbow Connection Number in Triangular Pyramids. In: 29th Workshop on Combinatorial Mathematics and Computation Theory, Taipei, Taiwan (2012)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Information Management, Chinese Culture University, Taipei, Taiwan, R.O.C.

    Fu-Hsing Wang, Ze-Jian Wu & Yann-Jong Hwang

Authors
  1. Fu-Hsing Wang
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  2. Ze-Jian Wu
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  3. Yann-Jong Hwang
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Corresponding author

Correspondence to Fu-Hsing Wang .

Editor information

Editors and Affiliations

  1. , Department of Computer Science and, National Dong Hwa University, #1, Sec. 2, Da Hsueh Rd., Hualien, Taiwan R.O.C.

    Ruay-Shiung Chang

  2. , Adjunct Professor, University of Canberra, Kirinari St. Mail Room, ACT, 2601, Australia

    Lakhmi C. Jain

  3. , Department of Computer Science and, National Dong Hwa University, #1, Sec. 2, Da Hsueh Rd., Hualien, Taiwan R.O.C.

    Sheng-Lung Peng

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© 2013 Springer-Verlag Berlin Heidelberg

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Wang, FH., Wu, ZJ., Hwang, YJ. (2013). An Upper Bound of the Rainbow Connection Number in RTCC Pyramids. In: Chang, RS., Jain, L., Peng, SL. (eds) Advances in Intelligent Systems and Applications - Volume 1. Smart Innovation, Systems and Technologies, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35452-6_3

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  • DOI: https://doi.org/10.1007/978-3-642-35452-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35451-9

  • Online ISBN: 978-3-642-35452-6

  • eBook Packages: EngineeringEngineering (R0)

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