Explicit relation between the Wiener index and the edge-Wiener index of the catacondensed hexagonal systems

Chen, Ailian; Xiong, Xianzhu; Lin, Fenggen

doi:10.1016/j.amc.2015.10.063

Cited by 10 publications

(7 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The edge-Wiener index of a graph was introduced in [21] as the Wiener index of the line graph and has been since then intensively investigated [1,3,6,12,20,27,28]. However, the concept was studied even before as the Wiener index of line graphs, see [4,17].…”

Section: Introductionmentioning

confidence: 99%

The edge-Wiener index and the edge-hyper-Wiener index of phenylenes

Pleteršek¹

2019

Discrete Applied Mathematics

View full text Add to dashboard Cite

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 the recent years. In this paper we consider the edge-Wiener index and the edge-hyper-Wiener index of phenylenes, which represent an important class of molecular graphs. For an arbitrary phenylene, four quotient trees based on the elementary cuts are defined in a similar way as it was previously done for benzenoid systems. The computation of the edge-Wiener index of the phenylene is then reduced to the calculation of the weighted Wiener indices of the corresponding quotient trees. Furthermore, a method for computing the edgehyper-Wiener index of phenylenes is described. Finally, the application of these results gives closed formulas for the edge-Wiener index and the edge-hyper-Wiener index of linear phenylenes.

show abstract

Section: Introductionmentioning

confidence: 99%

The edge-Wiener index and the edge-hyper-Wiener index of phenylenes

Pleteršek¹

2019

Discrete Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…For some of the recent discoveries on the edge-Wiener index the reader can refer to [6,20,21,24] and also to a survey paper [13]. Moreover, it is worth mentioning that the edge-Wiener index of any connected graph G is closely related to the edge-Hosoya polynomial [4] of G, defined as H e (G, x) = k≥0 d e (G, k) x k , where d e (G, k) denotes the number of (unordered) edge pairs at distance k.…”

Section: Introductionmentioning

confidence: 99%

Generalized cut method for computing the edge-Wiener index

Tratnik¹

2020

Discrete Applied Mathematics

View full text Add to dashboard Cite

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 edge-Wiener index, and the vertex-edge-Wiener index of weighted quotient graphs which are defined by a partition of the edge set that is coarser than Θ * -partition. Thus, already known analogous methods for computing the edge-Wiener index of benzenoid systems and phenylenes are greatly generalized. Moreover, reduction theorems are developed for the edge-Wiener index and the vertex-edge-Wiener index since they can be applied in order to compute a corresponding index of a (quotient) graph from the socalled reduced graph. Finally, the obtained results are used to find the closed formula for the edge-Wiener index of an infinite family of graphs.

show abstract

“…In the recent years, mathematical techniques for the computation of the edge‐Wiener index have been considered by a number of researchers, see the papers and a survey . Motivated by the vertex and edge versions of the Wiener indices, the vertex‐edge‐Wiener index was introduced in the paper and it is defined as the sum of distances between all pairs of G consisting of a vertex and an edge.…”

Section: Introductionmentioning

confidence: 99%

Edge Distance‐based Topological Indices of Strength‐weighted Graphs and their Application to Coronoid Systems, Carbon Nanocones and SiO₂ Nanostructures

Arockiaraj¹,

Klavžar

Clement³

et al. 2019

Molecular Informatics

View full text Add to dashboard Cite

The edge-Wiener index is conceived in analogous to the traditional Wiener index and it is defined as the sum of distances between all pairs of edges of a graph G. In the recent years, it has received considerable attention for determining the variations of its computation. Motivated by the method of computation of the traditional Wiener index based on canonical metric representation, we present the techniques to compute the edge-Wiener and vertex-edge-Wiener indices of G by dissecting the original graph G into smaller strength-weighted quotient graphs with respect to Djoković-Winkler relation. These techniques have been applied to compute the exact analytic expressions for the edge-Wiener and vertex-edge-Wiener indices of coronoid systems, carbon nanocones and SiO 2 nanostructures. In addition, we have reduced these techniques to the subdivision of partial cubes and applied to the circumcoronene series of benzenoid systems.

show abstract

Explicit relation between the Wiener index and the edge-Wiener index of the catacondensed hexagonal systems

Cited by 10 publications

References 9 publications

The edge-Wiener index and the edge-hyper-Wiener index of phenylenes

The edge-Wiener index and the edge-hyper-Wiener index of phenylenes

Generalized cut method for computing the edge-Wiener index

Edge Distance‐based Topological Indices of Strength‐weighted Graphs and their Application to Coronoid Systems, Carbon Nanocones and SiO₂ Nanostructures

Contact Info

Product

Resources

About

Explicit relation between the Wiener index and the edge-Wiener index of the catacondensed hexagonal systems

Cited by 10 publications

References 9 publications

The edge-Wiener index and the edge-hyper-Wiener index of phenylenes

The edge-Wiener index and the edge-hyper-Wiener index of phenylenes

Generalized cut method for computing the edge-Wiener index

Edge Distance‐based Topological Indices of Strength‐weighted Graphs and their Application to Coronoid Systems, Carbon Nanocones and SiO2 Nanostructures

Contact Info

Product

Resources

About

Edge Distance‐based Topological Indices of Strength‐weighted Graphs and their Application to Coronoid Systems, Carbon Nanocones and SiO₂ Nanostructures