# 臺灣博碩士論文加值系統

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 相似於 L(2,1)-標號 , 我們使用環狀差值來代替正規絕對差值 , 以研究圖形之距離為二的標號。
 Analogously to the L(a,b)-labelling , we study a new class of distance two labellings of graph by using the circular distance metric in stead of the linear distance metric (the Euclidean metric).
 Contents Abstract.......................................................I Contents......................................................II 1 Fundamental Concepts to Graphs...............................1 2 Circular Distance Two Labellings on Elementary Graph.........5 2.1 Introduction and Basic Properties........................5 2.2 Trees....................................................8 2.3 Cycles..................................................17 3 Labellings on The Join of Graphs............................27 3.1 The Constraints with Linear Distance : Revisited........27 3.2 The Constraints with Circular Distance on Complete multipartite Graph......................................34 Bibliography..................................................38
 1. J.S.Chen , The Circular Labelling on Cycles and the Zero Sum of a Sequence of Numbers , Master Thesis , Dept. of Applied Math. , Feng Chia Univ. , Taichung , Taiwan (1999).2. J. R. Griggs and R. K. Yeh , Labelling graphs with a condition at distance two} , SIAM J. Disc. Math. , 5 (1992) 586-595.3. J. P. Georges and D. W. Mauro , Generalized vertex labellings with a condition at distance two , Congr. Numer. , 109 (1995) 141-159.4. J. van den Heuvel , R. A. Leese and M. A. Shepherd , Graph labelling and radio channel assignment , J. Graph Theory , to appear.5. W. K. Hale , Frequency assignment : theory and applications , Proc. IEEE , 68 (1980) 1497-1514.6. D. D.-F. Liu , Relating Hamiltonicity and path covering to distance two labellings of graphs , manuscript.7. F. S. Robetrs , private communication with J. R. Griggs (1988).8. K.F.Wu , Circular L(d,1)-labellings on graphs , Master Thesis , Dept. of Applied Math. , Feng Chia Univ. , Taichung , Taiwan (1999).
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