Dendritic macromolecules’ have attracted much attention as organic examples of well-defined nanostructures. These molecules are ideal model systems for studying how physical properties depend on molecular size and architecture. In this paper using a simple result, some GAP programs are prepared to compute Wiener and hyper Wiener indices of dendrimers.

The recent discovery of boron triangular nanotubes competes with carbon in many respects. The closed form of M-polynomial of nanotubes produces closed forms of many degree-based topological indices which are numerical parameters of the structure and, in combination, determine properties of the concerned nanotubes. In this report, we give M-polynomials of boron triangular nanotubes and recover m...

Let G be a simple connected graph and di be the degree of its ith vertex. In a recent paper [D. Vukičević, B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem. 46 (2009) 1369–1376] the ‘‘first geometric–arithmetic index’’ of a graph Gwas defined as GA1 = − di dj (di + dj)/2 with summation going over all pairs of ...

In this note we give a new representation for closed sets under which the robust zero set of a function is computable. We call this representation the component cover representation. The computation of the zero set is based on topological index theory, the most powerful tool for finding robust solutions of equations.

The atom–bond connectivity index of a graph G is defined as

It is known that many integrable systems can be reduced from self-dual Yang-Mills equations. The formal solution space to the self-dual Yang-Mills equations is given by the so called ADHM construction, in which the solution space are graded by vector spaces with dimensionality concerning topological index. When we consider a reduced self-dual system such as the Bogomol’nyi equations, in terms o...

The Szeged index (Sz) is a recently proposed1q2 structural descriptor, based on the distances of the vertices of the molecular graph. In order to be able to study the properties of this novel topological index it would be advantageous to possess an easy method for its calculation. The calculation of Sz directly from its definition (see below) is quite cumbersome, especially in the case of large...

Solutions of physical equations which have non-trivial topological properties have been studied for already more than five years. As examples we may give the "monopole""2 and the ' ' in~tanton'~ in gauge field theories and the "pseudoparticle" in a two-dimensional isotropic f e r r ~ m a g n e t . ~ All these solutions a re characterized by some topological index: the magnetic charge of the mon...

let $g$ be a molecular graph with vertex set $v(g)$, $d_g(u, v)$ the topological distance between vertices $u$ and $v$ in $g$. the hosoya polynomial $h(g, x)$ of $g$ is a polynomial $sumlimits_{{u, v}subseteq v(g)}x^{d_g(u, v)}$ in variable $x$. in this paper, we obtain an explicit analytical expression for the expected value of the hosoya polynomial of a random benzenoid chain with $n$ hexagon...

Within the setting of infinite-dimensional self-dual CAR C* algebras describing fermions in [Formula: see text] lattice, we depart from well-known Araki–Evans index for quasi-free fermion states and rewrite it terms rather than basis projections. Furthermore, reformulate results that relate equivalences Fock representations to parity into Gel’fand–Naimark–Segal associated parity.