• Corpus ID: 58006474

On Extremal Graphs of Weighted Szeged Index

  title={On Extremal Graphs of Weighted Szeged Index},
  author={Jan Bok and Boris Furtula and Nikola Jedli{\vc}kov{\'a} and Riste {\vS}krekovski},
An extension of the well-known Szeged index was introduced recently, named as weighted Szeged index ($\textrm{sz}(G)$). This paper is devoted to characterizing the extremal trees and graphs of this new topological invariant. In particular, we proved that the star is a tree having the maximal $\textrm{sz}(G)$. Finding a tree with the minimal $\textrm{sz}(G)$ is not an easy task to be done. Here, we present the minimal trees up to 25 vertices obtained by computer and describe the regularities… 

Figures and Tables from this paper

Computing weighted Szeged and PI indices from quotient graphs
  • N. Tratnik
  • Mathematics
    International Journal of Quantum Chemistry
  • 2019
The weighted Szeged index and the weighted vertex-PI index of a connected graph $G$ are defined as $wSz(G) = \sum_{e=uv \in E(G)} (deg (u) + deg (v))n_u(e)n_v(e)$ and $wPI_v(G) = \sum_{e=uv \in E(G)}
Five results on maximizing topological indices in graphs
  • Stijn Cambie
  • Mathematics
    Discrete Mathematics & Theoretical Computer Science
  • 2021
In this paper, we prove a collection of results on graphical indices. We determine the extremal graphs attaining the maximal generalized Wiener index (e.g. the hyper-Wiener index) among all graphs
General cut method for computing Szeged‐like topological indices with applications to molecular graphs
Szeged, PI and Mostar indices are some of the most investigated distance-based molecular descriptors. Recently, many different variations of these topological indices appeared in the literature and
On graphs preserving PI index upon edge removal
The paper is concerned with the PI index of graphs. Let G be a graph and e its edge. If PI(G)=PI(G-e)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}
On Mostar index of trees with parameters
The Mostar index of a graph G is defined as the sum of absolute values of the differences between nu and nv over all edges uv of G, where nu and nv are respectively, the number of vertices of G
Trees with Minimum Weighted Szeged Index Are of a Large Diameter
It is shown a surprising property that these trees have maximum degree at most 16, and as a consequence, it is promptly concluded thatThese trees are of large diameter.
Studies on Graphical indices
We prove a selection of four results on graphical indices.


The Edge-Szeged Index and the PI Index of Benzenoid Systems in Linear Time
The edge-Szeged index of a graph $G$ is defined as $Sz_e(G) = \sum_{e=uv \in E(G)}m_u(e)m_v(e)$, where $m_u(e)$ denotes the number of edges of $G$ whose distance to $u$ is smaller than the distance
Graphs Having the Maximal Value of the Szeged Index
The Szeged index is a new topological index based on distances between vertices of a graph. A conjecture of Klavyzar, Rajapakse and Gutman concerning graphs with the maximal value of the Szeged index
Weighted Szeged Index of Graphs
The weighted Szeged index of a connected graph G is dened as Szw(G) = Σe=uv 2E(G)(dG(u) + dG(v))nGu(e) nGv(e); where nGu (e) is the number of vertices of G whose distance to the vertex u is less than
Weighted Szeged Index of Generalized Hierarchical Product of Graphs
The Szeged index of a graph G; denoted by Sz(G) = P uv=e2E(G) n G (e)n G (e): Similarly, theWeightedSzegedindexofagraphG;denotedbySzw(G) = P uv=e2E(G) d G(u)+ dG(v) n G (e)n G v (e); where dG(u) is
Notes on Trees with Minimal Atom-Bond Connectivity Index
If G =( V, E) is a molecular graph, and d(u) is the degree of its vertex u , then the atom– bond connectivity index of G is ABC = � uv∈E � [d(u )+ d(v) − 2]/[d(u) d(v)] . This molecular structure
Selected properties of the Schultz molecular topological index
  • I. Gutman
  • Mathematics
    J. Chem. Inf. Comput. Sci.
  • 1994
The nontrivial part of MTI is the quantity S, and the new notation is preferred because the symbol S can be associated with the name of th discoverer of the "molecular topological index".
In this paper, the weighted Szeged indices of Cartesian product and Corona product of two connected graphs are obtained. Using the results obtained here, the weighted Szeged indices of the hypercube
The weighted vertex PI index
Kragujevac Trees with Minimal Atom{Bond Connectivity Index
In the class of Kragujevac trees, the elements having minimal atom{bond connectivity index are determined. By this, an earlier conjecture [MATCH Commun. Math. Comput. Chem. 68 (2012) 131{136] is