Graphs and Combinatorics ( IF 0.7 ) Pub Date : 2020-01-10 , DOI: 10.1007/s00373-019-02126-y Helin Gong , Xian’an Jin , Mengchen Li
Let \(t_{i,j}\) be the coefficient of \(x^iy^j\) in the Tutte polynomial T(G; x, y) of a connected bridgeless and loopless graph G with order v and size e. It is trivial that \(t_{0,e-v+1}=1\) and \(t_{v-1,0}=1\). In this paper, we obtain expressions for another six extreme coefficients \(t_{i,j}\)’s with \((i,j)=(0,e-v)\),\((0,e-v-1)\),\((v-2,0)\),\((v-3,0)\),\((1,e-v)\) and \((v-2,1)\) in terms of small substructures of G. We also discuss their duality properties and their specializations to extreme coefficients of the Jones polynomial.
中文翻译:
图的Tutte多项式的几个极限系数
让\(T_ {I,J} \)是系数\(X ^ IY道^ J \)在TUTTE多项式Ť(ģ ; X, ÿ连接桥和无环图的)ģ与顺序v和大小Ë。\(t_ {0,e-v + 1} = 1 \)和\(t_ {v-1,0} = 1 \)是微不足道的。在本文中,我们获得了另外六个极限系数\(t_ {i,j} \)的表达式,其中\((i,j)= {0,ev)\),\((0,ev-1) \),\((v-2,0)\),\((v-3,0)\),\((1,ev)\)和\((v-2,1)\)就G的小子结构而言。我们还将讨论它们的对偶性质以及它们对琼斯多项式极值系数的专长。