If n+1 distinct points on the graph of a polynomial of degree n are given, the polynomial is uniquely determined. In the demonstration, the degree of the polynomial can be selected and then the necessary points are given. The graph corresponding the points is also plotted and it will ...
高次方程零点 与转折点的关系1The graph of every polynomial function of degree n has at most n-1 tur
Sketch the graph of the rational function y=(x^2-4)/(x^2-3). Sketch the graph of the rational function y=(x^4-1)/x^2. The graph of a polynomial function of degree n has, at most, (blank) turning points...
The present paper is addressed to the problem of determining under what conditions the characteristic polynomial of the adjacency matrix of a graph distinguishes between non-isomorphic graphs. A formula for the coefficients of the characteristic polynomial of an arbitrary digraph is derived, and the ...
We'll also pick a point between each pair of zeroes and again it doesn't really matter which points to pick so we'll just pick points that are near the middle of each pair of zeroes. Here are the function evaluations for this polynomial. We'll leave it to you to verify the ...
Polynomial Filters on Graphs The Graph Laplacian 给定一个graph G,用A来表示数值为0或者1的邻接矩阵,用D表示对角度矩阵(矩阵对角线数值表示与行node相邻node的数量),那么 D_{v}=\sum_{u} A_{v u}。graph Laplacian矩阵L可以表示为:L=D - A。右图的对角线就是行node的度数,负数是减去的邻接矩阵(蓝色...
Let P ( G ,λ) be the chromatic polynomial of a graph G with n vertices, independence number α and clique number ω. We show that for every λ?lt;i>n , ( )<sup>α</sup>?lt;a name="Equ3"> ?lt;a name="Equ4"> ( )<sup> n </sup> <sup>?lt;/sup>. We characterize th...
A New Recursion Relation for the Characteristic Polynomial of a Molecular Graph A recursion relation for the characteristic polynomial φ(G) of a molecular graph G is obtained, by means of which φ(G) is expressed as a linear combinati... VR Rosenfeld,I Gutman - 《Journal of Chemical Informa...
{1,...,n}.WedenotebyE(G)thesetofitsedges.AsubgraphofGobtainedby deletingvertexiandallitsincidentedgesiscalledavertex-deletedsubgraphofGand isdenotedbyG i .Thecollectionofvertex-deletedsubgraphsofGisknownasitsdeck. ThecharacteristicpolynomialofGisthecharacteristicpolynomialofitsadjacency matrixAandisdefinedb...
Draw the graph of the polynomial f(x)=x^3 . 02:23 If each one of the following graphs is the graph of a polynomial, then... 02:28 The graphs of y=a x^2+b x+c are given in Fig. Identify the signs of ... 09:32 Find the zeros of the quadratic polynomial f(x)=6x^2-3...