let $g$ be a simple graph of order $n$‎. ‎we consider the‎ ‎independence polynomial and the domination polynomial of a graph‎ ‎$g$‎. ‎the value of a graph polynomial at a specific point can give‎ ‎sometimes a very surprising information about the structure of the‎ ‎graph‎. ‎in this paper we investigate independence and domination‎ ‎polynomial at $-1$ and $1$‎.

in this work, the solution of a boundary value problem is discussed via asemi analytical method. the purpose of the present paper is to inspect theapplication of the adomian decomposition method for solving the nagumotelegraph equation. the numerical solution is obtained for some special casesso that demonstrate the validity of method.

n this paper, we apply picard’s iteration method followed by adomian decomposition method to solve a nonlinear singular cauchy problem of euler- poisson- darboux equation. the solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by carroll and showalter (1976)in the solution of singular cauchy problem.

we find an explicit expression of the tutte polynomial of an $n$-fan. we also find a formula of the tutte polynomial of an $n$-wheel in terms of the tutte polynomial of $n$-fans. finally, we give an alternative expression of the tutte polynomial of an $n$-wheel and then prove the explicit formula for the tutte polynomial of an $n$-wheel.

We study approximate solutions of a nonlinear integral equation of Hammerstein type. We describe the principle of discrete Adomian decomposition method (DADM). DADM is considered in the case we evaluate numerical integration by using Chebyshev roots. This technique gives an accurate solutions as will shown by illustrate examples.

By studying Adomian decomposition method as well as its adaptabilities and capabilities, and by providing experiments, this article attempts to examine the barriers that arise in the course of calculating the above algorithm and that deflect us from the true solution.

Adomian decomposition method has been employed to obtain solutions of a system of nonlinear fractional differential equations: D i yi (x)=Ni(x, y1, . . . , yn), y i (0)= c k, 0 k [ i ], 1 i n and D i denotes Caputo fractional derivative. Some examples are solved as illustrations, using symbolic computation. © 2005 Elsevier B.V. All rights reserved.

In this paper, Adomian method has been applied to approximate the solution of fuzzy volterra-fredholm integral equation. That, by using parametric form of fuzzy numbers, a fuzzy volterra-fredholm integral equation has been converted to a system of volterra-fredholm integral equation in crisp case. Finally, the method is explained with illustrative examples.

This paper presents a new symbolic algorithm to compute the singular initial value problem of second-order ordinary differential equations using Adomian decomposition method. The algorithm has been implemented in the computer algebra system Maple to facilitate the application of this method. A number of examples are presented to demonstrate the computation efficiency of the program. 2005 Elsevi...