19 research outputs found
The Theta polynomial Θ(G,x) and the Theta index Θ(G) of molecular graph Polycyclic Aromatic Hydrocarbons PAHk
The omega polynomial Ω(G,x), for counting qoc strips in molecular graph G was defined by Diudea as  with m(G,c), being the number of qoc strips of length c. The Theta polynomial Θ(G,x) and the Theta index Θ(G) of a molecular graph G were defined as Θ(G,x)= and Θ(G)=, respectively.In this paper, we compute the Theta polynomial Θ(G,x) and the Theta index Θ(G) of molecular graph Polycyclic Aromatic Hydrocarbons PAHk, for all positive integer number k.Â
Cacti with Extremal PI Index
The vertex PI index is a
distance-based molecular structure descriptor, where denotes the
number of vertices which are closer to the vertex than to the vertex
and which has been the considerable research in computational chemistry dating
back to Harold Wiener in 1947. A connected graph is a cactus if any two of its
cycles have at most one common vertex. In this paper, we completely determine
the extremal graphs with the largest and smallest vertex PI indices among all
the cacti. As a consequence, we obtain the sharp bounds with corresponding
extremal cacti and extend a known result.Comment: Accepted by Transactions on Combinatorics, 201
Computing GA_{5} index of armchair polyhex nanotube
The fifth geometric-arithmetic index of a graph is defined to be GA_5(G). This index was introduced by A. Graovac et al. in 2011. In this paper, we give explicit formulas for the fifth geometric-arithmetic index of a family of Hexagonal Nanotubes namely: Armchair Polyhex Nanotubes
Computing the Szeged and PI Indices of VC5C7[p,q] and HC5C7[p,q] Nanotubes
In this paper we give a GAP program for computing the Szeged and the PI indices of any graph. Also we compute the Szeged and PI indices of VC5C7 [ p,q] and HC5C7 [ p,q] nanotubes by this program
Computing the F-index of nanostar dendrimers
AbstractDendrimers are highly branched nanostructures and are considered a building block in nanotechnology with a variety of suitable applications. In this paper, a vertex degree-based topological index, namely, the F-index, which is defined as the sum of cubes of a graph's vertex degrees, is studied for certain dendrimers. In this study, we present exact expressions for the F-index and F-polynomial of six infinite classes of nanostar dendrimers
The vertex PI index and Szeged index of bridge graphs
AbstractRecently the vertex Padmakar–Ivan (PIv) index of a graph G was introduced as the sum over all edges e=uv of G of the number of vertices which are not equidistant to the vertices u and v. In this paper the vertex PI index and Szeged index of bridge graphs are determined. Using these formulas, the vertex PI indices and Szeged indices of several graphs are computed
Omega Polynomial in Tubular Nanostructures
A new counting polynomial, called the »Omega« Ω(G, x) polynomial, was recently proposed by Diudea on the ground of quasi-orthogonal cut »qoc« edge strips in a polycyclic graph. Within a qoc, not all cut edges are necessarily orthogonal, meaning not all are pairwise codistant. Two topological indices: CI (Cluj-Ilmenau), eventually equal to the well-known PI index, in planar, bipartite graphs, and IΩ are defined on the newly proposed polynomial and exemplified. Closed analytical formulas for Ω(G, x) and CI in polyhex tori and tubes are given
Embeddability of open-ended carbon nanotubes in hypercubes
AbstractA graph that can be isometrically embedded into a hypercube is called a partial cube. An open-ended carbon nanotube is a part of hexagonal tessellation of a cylinder. In this article we determine all open-ended carbon nanotubes which are partial cubes