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A modified Wiener number was proposed by Graovać and Pisanski. It is based on the full automorphism group of a graph. In this paper, we compute the difference between these topological indices for some polyhedral graphs. [ABSTRACT FROM AUTHOR]

The nullity of a graph is defined as the multiplicity of eigenvalue zero of graph G is named the nullity of G denoted by η(G). In this paper we investigate some properties of the nullity of some classes of graphs and then we compute the nullity of some infinite families of dendrimers. [ABSTRACT FROM AUTHOR]

In the present paper we study some properties of a new graph invariant named reciprocal degree distance of some molecular graphs. This new topological index is defined by Hua et al. as RDD(G) =∑u,v∊E(G) (d(u) + d(v))[d(u,v)]-1 , where the d(u,v) denotes the distance between vertices u and v. [ABSTRACT FROM AUTHOR]

Omega polynomial was introduced by Diudea. Following Omega polynomial, the Sadhana polynomial was defined by Ashrafi et al. In this paper we compute Omega and Sadhana polynomials of three classes of dendrimers. [ABSTRACT FROM AUTHOR]

One the most famous topological index is the Wiener index. It represents the sum of distances of a connected graph and was widely used in correlational studies involving various physical, chemical and biological properties. This topological index was introduced in 1947 by one of the pioneer of this area Harold Wiener. In the present paper, we compute the Wiener index of an infinite class of fullerenes. [ABSTRACT FROM AUTHOR]

Two edges e and f of a plane graph G are in relation opposite, e op f, if they are opposite edges of an inner face of G. Relation op enables the partition the edge set of G into opposite edge strips ops. On this ground, Diudea defined Omega and Theta polynomial while Ashrafi et al. defined the Sadhana polynomial. In this paper a weighted version of these polynomials was introduced and several relations between them are demonstrated. Some molecular weights are suggested in view of using the derived topological indices in correlational studies. [ABSTRACT FROM AUTHOR]

The eccentricity ε(u) is the largest distance between u and any other vertex x of G. The eccentric connectivity index ξ(G) of G is defined as ξ(G) = .... In this paper a new method is presented by which it is possible to compute the eccentric connectivity index of molecular graphs. We apply our method to compute the eccentric connectivity index of toroidal fullerenes. [ABSTRACT FROM AUTHOR]

The nullity of a graph is defined as the multiplicity of the eigenvalue zero in the spectrum of the adjacency matrix of the graph. In this paper we investigate the nullity of some classes of graphs. [ABSTRACT FROM AUTHOR]

Omega polynomial Ω(G, x) , defined by Diudea in Carpath. J. Math., 2006, 22, 43-47, counts topologically parallel edges eventually forming a strip of adjacent faces/rings, in a graph G=G(V,E). The first and second derivatives, in x=1, of Omega polynomial enables the evaluation of the Cluj-Ilmenau CI index. Analytical close formulas for the calculation of this polynomial in two hypothetical crystal-like lattices are derived. [ABSTRACT FROM AUTHOR]

The Omega polynomial Ω(x) was recently proposed by Diudea [Carpath. J. Math., 2006, 22, 43-47]. It is defined on the ground of "opposite edge strips" ops. The related polynomial: Sadhana Sd(x) can also be calculated by ops counting. In this paper we compute these polynomials for the ((4,7)3) infinite network, designed by Trs(Ca(4,4)) sequence of map operations. [ABSTRACT FROM AUTHOR]

Let m(G,c) be the number of strips of length c. The omega polynomial was defined by M. V. Diudea as Ω(G, x) =∑cm∙xc. One can obtain the Sadhana polynomial by replacing xc with x∣E∣-c in omega polynomial. Then the Sadhana index will be the first derivative of Sd(G,x) evaluated at x = 1. In this paper, the Omega and Sadhana polynomials of a new infinite class of fullerenes is computed for the first time [ABSTRACT FROM AUTHOR]

The Omega polynomial is defined as Ω(G,x) = Σs m· xs where m(G,s) is the number of ops strips of length s. Also, the Sadhana polynomial is defined as = Σs m(G,s)· x∣E∣-s . This last polynomial has been defined to evaluate the Sadhana index of a molecular graph. In this paper, the Omega and Sadhana polynomials of an infinite family of fullerenes is computed for the first time. [ABSTRACT FROM AUTHOR]

Hetero-fullerenes are fullerene molecules in which one or more carbon atoms are replaced by hetero-atoms such as boron or nitrogen, whose formation is a kind of "on-ball" doping of the fullerene cage. In this paper, the numbers of all C40n-kXk hetero-fullerenes are computed, where C40n is an infinite family of fullerenes. We apply the computer algebra system GAP to compute the number of permutational isomers of hetero-fullerenes of the C80 fullerene with D20 point group symmetry. [ABSTRACT FROM AUTHOR]