几类图的伴随多项式的整除性特征

用Ｐｎ和Ｃｎ依次表示有ｎ个顶点的路和圈．Ｄｎ表示Ｋ３的一个顶点与Ｐｎ－２的一个１度点重迭后得到的图．Ｔ（ｌ，ｍ，ｎ）表示度序列是（１，１，１，２，２，……，２，３）的树，其中ｌ，ｍ，ｎ分别是从它的唯一３度点到３个１度点的３条路的长．图Ｇ的伴随多项式记为ｈ（Ｇ，ｘ），本文证明了当Ｇ＝Ｐｎ，Ｃｎ，Ｄｎ，Ｔ（１，１，ｎ），Ｔ（１，２，ｎ），Ｔ（１，３，ｎ），Ｔ（１，４，ｎ）时，ｈ（Ｇ，ｘ）能被ｈ（Ｐｍ，ｘ）（ｍ≥２）整除的充要条件．

Division Character of Adjoint Polynomials of a Variety of Graph

Let P n denote the path with n vertices and C n denote the cycle with n vertices, Let D n denofe the graph obtained by identifying arbitrary vertex of K 3 with vertex of degree 1 of P n-2 ,the tree having degree sequence (1,1,1,2,2,……,2,3) is called a tree of T-shape, let T(l,m,n)denote the tree of T-shape, from which the lengths of the three paths come. The only vertex of degree 3 to three vertices of degree 1 are l,m,n respectively (1≤l≤m≤n).Let h(G,x) denote adjoint polynomials of graph, G.In this paper, we prove that division charecter of h(G,x) is divisible by h(P m,x),when G=P n,C n,D n,T(1,1,n),T(1,2,n),T(1,3,n),T(1,4,n).