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 本論文主要是介紹圖形學中的著色多項式(chromatic polynomials)，以及如何求得各圖形的著色多項式的方法。以下為此論文所應用的主要內容： 第一章：刪除-結合法(deletion-contraction method)。 第二章：介紹二部完全圖(complete bipartite graph)、錐圖(pyramid)及雙錐圖(double pyramid)的著色多項式。 第三章：利用圖的秩矩陣(rank matrix)求著色多項式。 第四章：介紹不可分的誘導子圖(non-separable induced subgraphs)的乘積表示式，並依此求得著色多項式。
 Chapter 0 :Introduction2 Chapter 1 :The deletion-contraction method7 1.1The definition of chromatic polynomial7 1.2Basic properties of chromatic polynomial8 1.3The deletion-contraction method9 Chapter 2:Chromatic polynomial of join of two graphs14 2.1Chromatic polynomial of the complete bipartite graph Km,n14 2.2Chromatic polynomial of the pyramid Wn and the double pyramid Πn16 Chapter 3 :The rank polynomial18 Chapter 4 :The multiplicative expansion23 4.1The non-separable subgraph expansion23 4.2The induced subgraph expansion25 Appendix30 Reference31
 [B1] Baker G.A. Linked-cluster expansion in graph-vertex coloration problem, JCT(B) 10(1971), 217-231.[B2] Biggs, N.L. Expansion of the chromatic polynomial, Discrete Math, 6(1973), 105-113.[B2-1] Biggs, N.L. On cluster expansions in graph theory and physics, Quart. J. Math. (Oxford) 29(1978), 159-173.[B3] Birkhoff and Lewis, Chromatic polynomials.Math. Soc.60 (1964), 355-451.[B3-1] Birkhoff, G.D. (1912) A determinant formula for the number ways of coloring a map. Ann. Math. 14, 42-46.[H1] Harary Frank. Graph theory. Chapter 12(1969) 145-148.[H2] Heawood, P. J. Map colour theorems. Quart.J.Math.24 (1890), 332-338.[K1] Kempe, A. B. On the geographical problem of four colors. Amer. J. Math.2 (1879), 193-204.[M1] May, K. O. The origin of four-color conjecture. Isis 56 (1965), 346-348.[N1] Norman Biggs. Algebraic graph theory. Part 2(1993) 63-80.[O1] Ore and Stemple, Numerical methods in the four color problem. Recent progress in Combinatorics (W. T. Tutte, ed.) Academic Press, New York, (1969).[R1] Rota, On the foundations of combinatorial theory, I: Theory of functions. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 2 (1964), 340-368.[T1] Tutte, W.T. On dichromatic polynomials, JCT 2(1967), 301-320.[W1-1] Whitney, H. (1932) A logical expansion in mathematics, Bull. Amer. Math. Soc. 38, 572-579.[W1-2] Whitney, H. (1932) The coloring of graphs, Ann. Math. 33, 688-718.[W1-3] Whitney, The coloring of graphs. Ann. Math. (2) 33 (1932), 688-718.
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