# 臺灣博碩士論文加值系統

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 本篇論文所探討的是增殖圖上的帶寬問題。 更詳細來說， 我們解決了有某些條件的常數增殖圖上的帶寬問題， 及提供一些增殖路徑圖的答案
 This thesis investigates the bandwidth problem for multiplications of graphs. In particular, we solve the bandwidth problem for constant multiplications of graphs with certain conditions. We also give solution to some multiplications of paths.
 Abstract ( in Chinese ) i Abstract ( in English ) ii Contents iii 1.Introduction 1 2.Bandwidths of constant multiplications of graphs 3 3.Bandwidths of multiplications of paths 6 Reference 12
 [1] P. Z. Chin, J.Chva'talova', A. K. Dewdney and N. E. Gibbs,The bandwidth problem for graphs and matrices--a survey,J. Graph Theory 6 (1982) 223--254.[2] P. Z. Chinn, Y. Lin and J. Yuan, The bandwidth of thecorona of two graphs, Cong. Numer. 91 (1992) 141--152.[3] P. Z. Chinn, Y. Lin, J. Yuan and K. Williams,Bandwidth of the composition of certain graphs powers, ArsCombin. 39 (1994) 167--173.[4] J. Chva'talova', Optimal labelingof a product of two graphs, Discrete Math. 11 (1975)249--253.[5] J. Chva'talova', On the bandwidthproblem for graphs, Ph.D. Thesis, Dept Combin Opt. Univ.Waterloo (1980).[6] M. R. Garey, R. L. Graham, D. S. Johnson and D. E. Knuth,Complexity results for bandwidth minimization, SIAM J.Appl. Math. 34 (1978) 477--495.[7] L. H. Harper, Optimal numberings and isoperimetricproblems on graphs, J. Combin. Theory 1 (1966) 385--393.[8] Y. L. Lai, J. Liu and K. Williams, Bandwidth for thesum of k graphs, Ars Combin. 37 (1994) 149--155.[9] Y. L. Lai and K. Williams, Bandwidth of the strongproduct of paths and cycles, Cong. Numer. 109 (1995)123--128.[10] Y. L. Lai and K. Williams, A survey of solved problemsand applications on bandwidth, edgesum, and profile of graphs,J. Graph Theory 31 (1999) 75--94[11] J. Liu and K. Williams, On bandwidth and edgesumfor the composition of two graphs, Discrete Math. 143(1995), no. 1-3, 159--166.[12] J. Liu, J. Wang and K. Williams, Bandwidth for the sumof two graphs, Cong. Numer. 82 (1991) 79--85.[13] C. H. Papadimitriou, The NP-completeness of the bandwidthminimization problem, Computing 16 (1976) 263--270.[14] K. Williams, On bandwidth for the tensor product ofpaths with complete bipartite graphs, Cong. Numer. 102 (1994) 183--190.[15] J. H. Yan, The bandwidth problem in cographs, Tamsui Oxf. J. Math. Sci. 13 (1997) 31--36
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