fullerenes are closed−cage carbon molecules formed by 12 pentagonal and n/2 – 10hexagonal faces, where n is the number of carbon atoms. patrick fowler in his lecture inmcc 2009 asked about the wiener index of fullerenes in general. in this paper werespond partially to this question for an infinite class of fullerenes with exactly 10ncarbon atoms. our method is general and can be applied to full...

This paper shows that the weighting coefficient matrices of the differential quadrature method (DQM) are centrosymmetric or skew-centrosymmetric if the grid spacings are symmetric irrespective of whether they are equal or unequal. A new skew centrosymmetric matrix is also discussed. The application of the properties of centrosymmetric and skew centrosymmetric matrix can reduce the computational...

We consider square matrices A that commute with a fixed square matrix K, both with entries in a field F not of characteristic 2. When K2 = I, Tao and Yasuda defined A to be generalized centrosymmetric with respect to K. When K2 = −I, we define A to be pseudo-centrosymmetric with respect to K; we show that the determinant of every even-order pseudo-centrosymmetric matrix is the sum of two square...

Every n×n generalized K-centrosymmetric matrix A can be reduced into a 2× 2 block diagonal matrix (see [20]). This block diagonal matrix is called the reduced form of the matrix A. In this paper we further investigate some properties of the reduced form of these matrices and discuss the square roots of these matrices. Finally exploiting these properties, the development of structure-preserving ...

An $n\times n$ matrix $C$ is said to be {\it centrosymmetric} if it satisfies the relation $JCJ=C$, where $J$ counteridentity matrix. Centrosymmetric matrices have a rich eigenstructure that has been studied extensively in literature. Many results for centrosymmetric generalized wider classes of arise wide variety disciplines. In this paper, we obtain interesting spectral properties nonnegative...

The behaviour of the Flack parameter for centrosymmetric and pseudo-centrosymmetric crystal structures based on crystal structures published as being non-centrosymmetric is presented. It is confirmed for centrosymmetric structures that the value obtained for the Flack parameter is critically dependent on the Friedel coverage of the intensity data, approaching 0.5 for a coverage of 100% and stic...