Related papers: The hyper Wiener index of one pentagonal carbon na…
In this note, we introduce a new topological index of a graph G that we term peripheral hyper-Wiener index, denoted PWW(G). It is a natural extension of the peripheral Wiener index PW(G) initiated in [NB17] and is to the peripheral Wiener…
The edge-hyper-Wiener index of a connected graph $G$ is defined as $WW_e(G) = \frac{1}{2}\sum_{\lbrace e,f\rbrace \subseteq E(G)}d(e,f) + \frac{1}{2}\sum_{\lbrace e,f\rbrace \subseteq E(G)}d(e,f)^2$. We develop a method for computing the…
The Wiener index W(G) of a connected graph $G$ is the sum of distances between all pairs of vertices in G$. In this paper, we first give the recurrences or explicit formulae for computing the Wiener indices of spiro and polyphenyl hexagonal…
We report on various nanocarbons formed from a unique structural pattern containing two pentagons, three hexagons and two heptagons, resulting from local rearrange- ments around a divacancy in pristine graphene or nanotubes. This defect can…
The Graovac-Pisanski index, which is also called the modified Wiener index, considers the symmetries and the distances in molecular graphs. Carbon nanotubes are molecules made of carbon with a cylindrical structure possessing unusual…
Given a simple connected undirected graph G, the Wiener index W(G) of G is defined as half the sum of the distances over all pairs of vertices of G. In practice, G corresponds to what is known as the molecular graph of an organic compound.…
In this paper, we consider a molecular descriptor called the Wiener polarity index, which is defined as the number of unordered pairs of vertices at distance three in a graph. Molecular descriptors play a fundamental role in chemistry,…
The Wiener index is one of the oldest graph parameter which is used to study molecular-graph-based structure. This parameter was first proposed by Harold Wiener in 1947 to determining the boiling point of paraffin. The Wiener index of a…
Besides the well known Wiener index, which sums up the distances between all the pairs of vertices, and the hyper-Wiener index, which includes also the squares of distances, the edge versions of both indices attracted a lot of attention in…
Graph theory provides powerful tools for modeling concepts in number theory, leading to the introduction of graphs derived from arithmetic properties. One such structure is the divisor prime graph, $G_{Dp(n)}$. For any positive integer $n$,…
The edge-Wiener index of a connected graph $G$ is defined as the Wiener index of the line graph of $G$. In this paper it is shown that the edge-Wiener index of an edge-weighted graph can be computed in terms of the Wiener index, the…
The Wiener index of a (hyper)graph is calculated by summing up the distances between all pairs of vertices. We determine the maximum possible Wiener index of a connected $n$-vertex $k$-uniform hypergraph and characterize for every~$n$ all…
Carbon nanotube Y-junctions are of great interest to the next generation of innovative multi-terminal nanodevices. Topological indices are graph-theoretically based parameters that describe various structural properties of a chemical…
We propose a model for nanoscale supercapacitor consisting of two-dimensional insulating BN layers placed between two commensurate and metallic graphene layers. First-principles Density Functional calculations of structure optimized total…
Topological indices are parameters associated with graphs that have many applications in different areas such as mathematical chemistry. Among various topological indices, the Wiener index is classical \cite{w}. In this paper, we prove a…
The Wiener index $W(G)$ of a graph $G$ is one of the most well-known topological indices, which is defined as the sum of distances between all pairs of vertices of $G$. The diameter $D(G)$ of $G$ is the maximum distance between all pairs of…
The edge-Wiener index $W_e(G)$ of a connected graph $G$ is the sum of distances between all pairs of edges of $G$. A connected graph $G$ is said to be a cactus if each of its blocks is either a cycle or an edge. Let $\mathcal{G}_{n,t}$…
The Wiener polarity index of a graph is defined as the number of unordered pairs of vertices at distance three. In recent years, this topological index was extensively studied since it has many known applications in chemistry and also in…
Let $G=(V(G),E(G))$ be a molecular graph, where $V(G)$ and $E(G)$ are the sets of vertices (atoms) and edges (bonds). A topological index of a molecular graph is a numerical quantity which helps to predict the chemical/physical properties…
The paper discusses the edge hyper-Zagreb index of a graph, which is calculated by replacing vertex degrees with edge degrees. The degree of an edge is determined by adding up the degrees of the end vertices of the edge and subtracting 2.…