English
Related papers

Related papers: Graphs with the second and third maximum Wiener in…

200 papers

The Wiener index (the distance) of a connected graph is the sum of distances between all pairs of vertices. In this paper, we study the maximum possible value of this invariant among graphs on $n$ vertices with fixed number of blocks $p$.…

Discrete Mathematics · Computer Science 2019-05-08 Stéphane Bessy , François Dross , Katarína Hriňáková , Martin Knor , Riste Škrekovski

The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices. A connected graph is Eulerian if its vertex degrees are all even. In [Gutman, Cruz, Rada, Wiener index of Eulerian Graphs, Discrete…

Combinatorics · Mathematics 2021-01-22 Peter Dankelmann

The Wiener index of a connected graph is the sum of the distances between all pairs of vertices in the graph. It was conjectured that the Wiener index of an $n$-vertex maximal planar graph is at most $\lfloor\frac{1}{18}(n^3+3n^2)\rfloor$.…

Combinatorics · Mathematics 2019-12-09 Debarun Ghosh , Ervin Győri , Addisu Paulos , Nika Salia , Oscar Zamora

The distance of a vertex in a graph is the sum of distances from that vertex to all other vertices of the graph. The Wiener index of a graph is the sum of distances between all its unordered pairs of vertices. A graph has been obtained that…

Combinatorics · Mathematics 2024-07-16 Dinesh Pandey

The Wiener index of a connected graph is defined as the sum of the distances between all unordered pair of its vertices. In this paper, we characterize the graphs which extremize the Wiener index among all graphs on $n$ vertices with $k$…

Combinatorics · Mathematics 2019-08-01 Dinesh Pandey , Kamal Lochan Patra

Let $G$ be a connected graph of order $n$.The Wiener index $W(G)$ of $G$ is the sum of the distances between all unordered pairs of vertices of $G$. In this paper we show that the well-known upper bound $\big( \frac{n}{\delta+1}+2\big) {n…

Combinatorics · Mathematics 2023-06-22 Peter Dankelmann , Alex Alochukwu

The Wiener index (i.e., the total distance or the transmission number), defined as the sum of distances between all unordered pairs of vertices in a graph, is one of the most popular molecular descriptors. In this article we summarize some…

Combinatorics · Mathematics 2015-10-06 Martin Knor , Riste Škrekovski , Aleksandra Tepeh

The Wiener index of a connected graph is the sum of the distance of all pairs of distinct vertices. It was introduced by Wiener in 1947 to analyze some aspects of branching by fitting experimental data for several properties of alkane…

Combinatorics · Mathematics 2020-01-10 Peter Luo , Cun-Quan Zhang , Xiao-Dong Zhang

Over all graphs (or unicyclic graphs) of a given order, we characterise those graphs that minimise or maximise the number of connected induced subgraphs. For each of these classes, we find that the graphs that minimise the number of…

Combinatorics · Mathematics 2019-09-18 Audace A. V. Dossou-Olory

The Wiener index of a connected graph is the summation of all distances between unordered pairs of vertices of the graph. In this paper, we give an upper bound on the Wiener index of a $k$-connected graph $G$ of order $n$ for integers…

Combinatorics · Mathematics 2018-11-08 Zhongyuan Che , Karen L. Collins

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…

Combinatorics · Mathematics 2023-02-20 Stijn Cambie , Ervin Győri , Nika Salia , Casey Tompkins , James Tuite

The Wiener index of a connected graph is the sum of topological distances between all pairs of vertices. Since Wang gave a mistake result on the maximum Wiener index for given tree degree sequence, in this paper, we investigate the maximum…

Combinatorics · Mathematics 2009-07-23 Xiao-Dong Zhang , Yong Liu , Min-Xian Han

The Wiener index of a graph is the sum of the distances between all pairs of vertices, it has been one of the main descriptors that correlate achemical compound's molecular graph with experimentally gathered data regarding the compound's…

Combinatorics · Mathematics 2007-09-12 Hua Wang

Let $G$ be a a connected graph. The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices. We provide asymptotic formulae for the maximum Wiener index of simple triangulations and…

Combinatorics · Mathematics 2023-06-22 Éva Czabarka , Peter Dankelmann , Trevor Olsen , László A. Székely

The Wiener index of a graph is the sum of all the distances between any pair of vertices. We aim to describe graphs which minimize the Wiener index among all unicyclic graphs with fixed girth and given degree sequence. Depending on where…

Combinatorics · Mathematics 2024-10-29 Alewyn P. Burger , Valisoa R. M. Rakotonarivo

The Wiener index is defined as the sum of distances between all unordered pairs of vertices in a graph. It is one of the most recognized and well-researched topological indices, which is on the other hand still a very active area of…

Combinatorics · Mathematics 2023-03-22 Martin Knor , Riste Škrekovski , Aleksandra Tepeh

The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices. We provide formulae for the minimum Wiener index of simple triangulations and quadrangulations with connectivity at least $c$, and…

Combinatorics · Mathematics 2021-12-23 Éva Czabarka , Trevor Olsen , Stephen Smith , László A. Székely

The Wiener index of a connected graph is defined as the sum of distances between all its unordered pairs of vertices. Characterising graphs on $n$ vertices with a fixed diameter that maximise the Wiener index is a long-standing open…

Combinatorics · Mathematics 2026-05-26 Dinesh Pandey , Peruvemba Sundaram Ravi

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…

Combinatorics · Mathematics 2019-04-09 Niko Tratnik

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…

Combinatorics · Mathematics 2024-03-04 Junfeng An , Yingzhi Tian
‹ Prev 1 2 3 10 Next ›