On Extreme Coefficients Of The Tutte And Jones Polynomials Of Graphs

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 ti,j be the coefficient of xiyj in the Tutte polynomial T(x,y)of G.With the aid of bond lattice and circuit lattice,we first revise the expressions of to,m-n-1 and tl,m-n-1 obtained by Gong and Jin,and then obtain t0,m-n-2 and tn-4,0.Using the relation between the Jones polynomial and the Thtte polynomial,we check some known results on the extreme coefficients of Jones polynomials and further obtain coefficients of t|E|-3,t2 and t3.