Suppose ai indicates the number of orbits size i in graph G. A new counting polynomial, namely an orbit is defined as OG(x) = ?i aixi. Its modified version obtained by subtracting polynomial from 1. In present paper, we studied conditions under which integer can arise a graph. Additionally, surveyed graphs with small and characterized several classes respect to their polynomials.

This paper studies the application of principal component analysis, multiple polynomial regression, and artificial neural network ANN techniques to the quantitative analysis of binary mixture of dye solution. The binary mixtures of three textile dyes including blue, red and yellow colors were analyzed by PCA-Multiple polynomial Regression and PCA-Artificial Neural network PCA-ANN methods. The o...

In this paper, a remedial measure is first proposed to eliminate the effect of autocorrelation in phase-ІІ monitoring of autocorrelated polynomial profiles, where there is a first order autoregressive (AR(1)) relation between the error terms in each profile. Then, a control chart based on the generalized linear test (GLT) is proposed to monitor the coefficients of polynomial profiles and an R-c...

In the present work, the effects of operating conditions including pH, transmembrane pressure, oil concentration, and temperature on fouling resistance and the rejection of turbidity for a polymeric membrane in an ultrafiltration system of wastewater treatment were studied. A new modeling technique called evolutionary polynomial regression (EPR) was investigated. EPR is a method based on regres...

We study polynomial functors over locally cartesian closed categories. After setting up the basic theory, we show how polynomial functors assemble into a double category, in fact a framed bicategory. We show that the free monad on a polynomial endofunctor is polynomial. The relationship with operads and other related notions is explored. Introduction Background. Notions of polynomial functor ha...

The harmonic index H(G) , of a graph G is defined as the sum of weights 2/(deg(u)+deg(v)) of all edges in E(G), where deg (u) denotes the degree of a vertex u in V(G). In this paper we define the harmonic polynomial of G. We present explicit formula for the values of harmonic polynomial for several families of specific graphs and we find the lower and upper bound for harmonic index in Caterpill...