The Fibonacci Edge Labelings on Fibonacci Trees

피보나치트리에서 피보나치 에지 번호매김방법

  • 김용석 (서남대학교 컴퓨터정보통신)
  • Published : 2009.12.15

Abstract

In this paper, we propose seven edge labeling methods. The methods produce three case of edge labels-sets of Fibonacci numbers {$F_k|k\;{\geq}\;2$}, {$F_{2k}|k\;{\geq}\;1$} and {$F_{3k+2}|k\;{\geq}\;0$}. When a sort of interconnection network, the circulant graph is designed, these edge labels are used for its jump sequence. As a result, the degree is due to the edge labels.

본 논문에서는 임의의 피보나치 트리에 에지번호매김을 하여 피보나치 수들의 집합 {$F_k|k\;{\geq}\;2$}, {$F_{2k}|k\;{\geq}\;1$} 그리고 {$F_{3k+2}|k\;{\geq}\;0$}인 세가지 경우의 에지번호 집합을 얻는 7가지의 에지번호매김방법들을 제안한다. 이러한 에지번호들의 집합은 상호연결망의 일종인 원형군의 설계시 점프열로 사용할 수 있으므로 망척도 중 하나인 분지수를 결정한다.

Keywords

References

  1. F. T. Leighton, Introduction to Parallel Algorithms and Architectures: arrays, trees, hypercubes, Morgan Kaufmann Publishers, San Mateo, California, 1992.
  2. S. N. Bhatt, F. R. K. Chung, F. T. Leighton, and A. L. Rosenberg, "Efficient embeddings of trees in hypercubes," SIAM J. Compt., 21, pp.151-162, 1992.
  3. F. R. K. Chung, "On optimal linear arrangment of tree," Comput. Math. Appl. 10, pp.43-60, 1984. https://doi.org/10.1016/0898-1221(84)90085-3
  4. H.-S. Lim, On the Labelings of Graphs and their Aplications, Ph.D.Thesis, Dept. Compuetr Science, KAIST, 1993.
  5. KAIST, A Study on the Design and Development of a High-Performance Parallel Compuetr, 1th annual report, 1993.
  6. H.-S.Lim, J.-H.Park, and K.-Y.Chaw, "Embedding trees in recursive circulants," Discrete Applied Mathematics, 69, pp.83-99, 1996. https://doi.org/10.1016/0166-218X(95)00078-6
  7. Y.-S. Kim, "The Researh of Q-ege Labeling on Binomial Trees related to the Graph Embedding," IEEK J. CI. vol.42, Jan. pp,27-34, 2005.
  8. E. Horowitz, S. Sahni, and S. Anderson-Freed Fundamentals of Data Strutures in C. Computer Sience Press, p.493, 1993.
  9. W.-J. Hsu, "Fibonacci cubes-A new Interconnection Topology," IEEE Transactions on Parallel and Distributed Systems, vol.4, no.1, Jan. 1993.
  10. Y. -S. Kim, M. -G. Roo, "Postorder Fibonacci Circulants," KIPS J., vol,15-A, no.1, pp.27-34, 2008 https://doi.org/10.3745/KIPSTA.2008.15-A.1.27
  11. Y.-S. Kim, "The Embedding on Postorder Fibonacci Circulant," KIPS J., vol. 14-A, no.4, pp.249-284, 2008.
  12. R. L. Graham, D. E. Knuth, and O. Patashnik, "Special numbers," in Concrete Mathmatics. Reading, MA: Adisson-Wesley, 1989, ch.6.