中文摘要
本研究是要建構存在於超正方體中的非同構路徑，並計算總數。在製造與搜尋過程中，因為路徑的數量會隨著維度增高而劇烈爆增，使得一般的演算法無法應付，在這種狀況下所使用的製造與搜尋方法就會顯得相當重要。本論文提出一種有效率的製造與搜尋方法，並以截然不同的資料結構完成了兩個程式，它們皆以C語言編成。

Abstract
In this research we construct all non-isomorphic paths in the n-dimensional hypercube, and count the number of them. As the dimension n gets higher, the amount of the paths increases extremely large. So a normal algorithm cannot handle this situation. That is why we need to design a new method to construct and search non-isomorphic paths. This thesis offers an efficient algorithm to construct and search non-isomorphic paths. Two computer programs for solving the same problem are given here by using two different data structures. Both of them are programming by C.

參考文獻
[1]I.A. Campbell, J.M. Flesselles, R. Jullien and R. Botet, Random walks on a hypercube and spin glass relaxation, J. Phys. C: Solid State Phys.20(1987) L47.

[2]M-S. Chen, K. G. Shin, Message routing in an injured hypercube, Proceeding C3P Proceedings of the third conference on Hypercube concurrent computers(1998) 312-317.

[3]E. Chow, H. Madan, J. Peterson, D. Grunwald, D. Reed, Hyperswitch network for thehypercube computer, Proceeding ISCA '88 Proceedings of the 15th Annual International Symposium on Computer architecture16(May 1988) 90-99.

[4]F. Harary, J. P. Hayes, H.-J. Wu,A survey of the theory of hypercube graphs,Computers & Mathematics with Applications15(1988) 277-289.

[5]J.P. Hayes, T.N. Mudge and Q.F. Stout, Architecture of a hypercube supercomputer, Proc. 1986 International Conference on Parallel Processing (Aug. 1986) 653-660.

[6]J.P. Hayes and T. Mudge, Hypercube supercomputers, Proceedings of the IEEE 77 (1989) 1829-1841.

[7]S.Y. Hsieh, C.H. Chen, Pancyclicity on M¨obius cubes with maximal edgefaults, Parallel Comput.30(2004)407-421.

[8]L.-H. Hsu, S.-C.Liu and Y.-N. Yeh, Hamiltonicity of hypercubes with a constraint of required and faulty Edges, Journal of Combinatorial Optimization. 14no. 2-3(2007) 197-204.

[9]C.N. Hung, Y.H. Chang, C.M Sun, Longest paths and cycles in faulty hypercubes, Proceeding of the IASTED ICPDCN(2006)101-110.

[10]C.-N. Hung and Y.-J. Lai, The Hamiltonian cycle passing through prescribed edges in hypercubes with adjacently faulty vertices, Proceedings of the 26th Workshop on Combinatorial Mathematics and Computation Theory(2009) 187-193.

[11]T.K. Li, C.H. Tsai, J. J.M. Tan, L.H. Hsu, Bipanconnectivity and edge-fault- tolerant bipancyclicityof hypercubes, Information ProcessingLetters 87(2003)107-110.

[12]M. Ma, G. Liu, X. Pan, Path embedding in faulty hypercubes, Applied arithmetics and Computation192(Sep. 2007) 233-238.

[13]Y. Saad, M.H Schultz,Topological properties of hypercubes, IEEE Transactions on Computers37(2002) 867–872.

[14]C.-H.Tsai, J.J.M. Tan, T. Liang and L.-H. Hsu, Fault-tolerant hamiltonian laceability of hypercubes, Information Processing Letters 83(2002) 301-306.

[15]A. Wagner, Embedding arbitrary binary trees in a hypercube, Journal of Parallel and Distributed Computing7(Dec. 1989) 503-520.

[16]D. Wang, Embedding Hamiltonian cycles into folded hypercubes with faulty links, Journal of Parallel and Distributed Computing 61(2001) 545-564.

[17]D. Wang and Z. Wang, Minimum assignment of test links for hypercubes with lower fault bounds,J. Parallel Distrib. Comput.40(Feb. 1997) 185–193.

[18]D.B. West, Introduction to Graph Theory, second edition Prentice Hall, 2001.

[19]R. Wilson, Introduction to Graph Theory, fifth editionPrentice Hall, 2010.

[20]M.C. Yang, T.K. Li, J. J.M. Tan, L.H. Hsu, Fault tolerant cycle-embedding ofcrossed cubes, Information Processing Letters 88 (2003)149-154.