On extreme coefficients of the Tutte and Jones polynomials of graphs

本文研究了无割边无环的连通图G=(V，E)的Tutte多项式和Jones多项式的极端项系数。设t_{i，j}为图G的Tutte多项式T(G;x，y)中x^iy^j项的系数。我们通过色多项式的圈格和流多项式的键格的第0层至第3层元素，修正了已知结果t_{0，m−n−1}及t_{1，m−n−1}的值，并且得到了t_{0，m−n−2}和t_{n−4，0}。利用Jones多项式与Tutte多项式的关系，将Tutte多项式极端项的系数特殊化到Jones多项式，验证了已知结果，并进一步给出了Jones多项式中t_{|E|&...In this paper, we study expressions of several extreme coefficients of the Tutte and Jones polynomials of a graph G, which is bridgeless, loopless and connected. Let t_i,j bethecoefficientof x^iy^j intheTuttepolynomial T(x,y) of G. Withtheaid of bond lattice and circuit lattice, we first revise the expressions of t_{0,m−n−1} and t_{1,m−n−1} obtained by Gon...学位：理学硕士院系专业：数学科学学院_应用数学学号：1902014115262