Browse > Article

The Research of Q-edge Labeling on Binomial Trees related to the Graph Embedding  

Kim Yong-Seok (Department of Computer and Information Communications, Chonbuk Seonam University)
Publication Information
Journal of the Institute of Electronics Engineers of Korea CI / v.42, no.1, 2005 , pp. 27-34 More about this Journal
Abstract
In this paper, we propose the Q-edge labeling method related to the graph embedding problem in binomial trees. This result is able to design a new reliable interconnection networks with maximum connectivity using Q-edge labels as jump sequence of circulant graph. The circulant graph is a generalization of Harary graph which is a solution of the optimal problem to design a maximum connectivity graph consists of n vertices End e edgies. And this topology has optimal broadcasting because of having binomial trees as spanning tree.
Keywords
circulant graph; graph embedding; binomial tree; edge labeling; optimal broadcasting tree;
Citations & Related Records
연도 인용수 순위
  • Reference
1 F.T.Leighton, Introduction to parallel algorithms and architectures: arrays, trees, hyper -cubes, Morgan Kaufmann publishers, San Mateo, California, 1992
2 J. A. Bondy and U. S. R. Murty, Graph theory with applications, North-Holland, New York, 1976
3 Y. Yang and J. Wangr, Routing Permutations with link-disjoint and node-disjoint paths in a class of self-routable interconnects, IEEE trans. Parallel and Distributed Systems, vol. 14, no. 4, pp. 383-393, Apr. 2003   DOI   ScienceOn
4 H.-S. Lim, On the Labelings of Graphs and their Applications, Ph.D. Thesis, Dept. Computer Science, KAIST, 1993
5 F. R. K. 'Some problems and results in labelings of graphs,' The Theory and Application of graphs, G. Chartrand. ed., Wiley, New York (1981) pp. 255-263
6 S. W. Golomb, 'How to number a graph,' Graph Theory and Computing, Academic Press, New York (1972) pp. 23-37
7 D. A. Reed and H. A. Fujimoto, Multicomputer Networks: Massage-based Parallel Processing, M IT Press, 1987
8 M. R. Brown, Implementation and analysis of binomial queue algorithms, SIAM J. Comput. 7 (1978) pp. 298-319   DOI
9 V. M. Lo, S. Rajopadhye, S. Gupta, D. Keldsen, M. A. Mohamed and J. Telle, Mapping Divide-and-Conquer Algorithms to Parallel Architectures, Proc. of the 1990 International Conf. on Parallel Procesing, Vol. III, pp. 128-135 Aug. 1990
10 W. J. Hsu, C. B. Page and J. S. Liu, Computing Prefixes on a Large Family of Interconnection Topologies, Proc. of the 1992 International Conf. on Parallel Processing, Vol. III, pp. 153-159, Aug. 1992
11 F. Harary, The maximum connectivity of a graph, Proc. Nat. Acad. Sci. U. S. A., Vol. 48, pp. 1142-1146, 1962   DOI   ScienceOn
12 J.-H. Park, Circulant Graphs and their Application to Communication Networks, Ph.D. Thesis, Dept. Computer Science, KAIST, 1992
13 박정흠, 좌경룡, 재귀원형군과 하이퍼큐브의 임베딩, 정보과학회 논문지, 제22권 A편, 제12호, 1736-1741쪽, 1995년 12월
14 L. H. harper, Optimal numbering and isoperimetric problems on graph, J. Combiantorial Theory 1 (1966) pp. 385-393