scholarly journals Exact Formula and Improved Bounds for General Sum-Connectivity Index of Graph-Operations

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 167290-167299 ◽  
Author(s):  
Maqsood Ahmad ◽  
Muhammad Saeed ◽  
Muhammad Javaid ◽  
Muhammad Hussain
Keyword(s):  
Exact Formula ◽  
Connectivity Index ◽  
Graph Operations

scholarly journals Some inequalities for the atom-bond connectivity index of graph operations

2011 ◽  
Vol 159 (13) ◽  
pp. 1323-1330 ◽  
Author(s):  
G.H. Fath-Tabar ◽  
B. Vaez-Zadeh ◽  
A.R. Ashrafi ◽  
A. Graovac
Keyword(s):  
Connectivity Index ◽  
Graph Operations ◽  
Atom Bond

scholarly journals Vertex-Based Topological Indices of Double and Strong Double Graph of Dutch Windmill Graph

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Muhammad Asad Ali ◽  
Muhammad Shoaib Sardar ◽  
Imran Siddique ◽  
Dalal Alrowaili
Keyword(s):  
Graph Theory ◽  
Chemical Properties ◽  
Topological Indices ◽  
Connectivity Index ◽  
Vaporization Enthalpy ◽  
Zagreb Index ◽  
Graph Operations ◽  
Big Graphs ◽  
Physical And Chemical ◽  
Atom Bond

A measurement of the molecular topology of graphs is known as a topological index, and several physical and chemical properties such as heat formation, boiling point, vaporization, enthalpy, and entropy are used to characterize them. Graph theory is useful in evaluating the relationship between various topological indices of some graphs derived by applying certain graph operations. Graph operations play an important role in many applications of graph theory because many big graphs can be obtained from small graphs. Here, we discuss two graph operations, i.e., double graph and strong double graph. In this article, we will compute the topological indices such as geometric arithmetic index GA , atom bond connectivity index ABC , forgotten index F , inverse sum indeg index ISI , general inverse sum indeg index ISI α , β , first multiplicative-Zagreb index PM 1   and second multiplicative-Zagreb index PM 2 , fifth geometric arithmetic index GA 5 , fourth atom bond connectivity index ABC 4 of double graph, and strong double graph of Dutch Windmill graph D 3 p .

scholarly journals Sharp Bounds on the Augmented Zagreb Index of Graph Operations

2020 ◽  
Vol 44 (4) ◽  
pp. 509-522
Author(s):  
N. DEHGARDI ◽  
H. ARAM
Keyword(s):  
Simple Graph ◽  
Connectivity Index ◽  
Regular Graphs ◽  
Zagreb Index ◽  
Sharp Bounds ◽  
Graph Operations ◽  
Degree Of A Vertex ◽  
Augmented Zagreb Index ◽  
Composition Product ◽  
Product Of Graphs

Let G be a finite and simple graph with edge set E(G). The augmented Zagreb index of G is ( ) ∑ dG (u )dG (v) 3 AZI (G ) = ---------------------- , dG (u ) + dG (v) − 2 uv∈E(G ) where dG(u) denotes the degree of a vertex u in G. In this paper, we give some bounds of this index for join, corona, cartesian and composition product of graphs by general sum-connectivity index and general Randić index and compute the sharp amount of that for the regular graphs.

scholarly journals Computing bounds for the general sum-connectivity index of some graph operations

2020 ◽  
Vol 29 (2) ◽  
pp. 147-160
Author(s):  
S. Akhter ◽  
◽  
R. Farooq ◽  
Keyword(s):  
Connectivity Index ◽  
Graph Operations

Application of Corona Product of Graphs in Computing Topological Indices of Some Special Chemical Graphs

2017 ◽  
pp. 82-101
Author(s):  
Nilanjan De
Keyword(s):  
Topological Indices ◽  
Connectivity Index ◽  
Eccentric Connectivity Index ◽  
Molecular Graphs ◽  
Mathematical Chemistry ◽  
Graph Operations ◽  
Eccentricity Index ◽  
Chemical Graphs ◽  
Product Of Graphs ◽  
Corona Product

Graph operations play a very important role in mathematical chemistry, since some chemically interesting graphs can be obtained from some simpler graphs by different graph operations. In this chapter, some eccentricity based topological indices such as the total eccentricity index, eccentric connectivity index, modified eccentric connectivity index and connective eccentricity index and their respective polynomial versions of corona product of two graphs have been studied and also these indices of some important classes of chemically interesting molecular graphs are determined by specializing the components of corona product of graphs.

On Hyper-Zagreb Index of Three Graph Operations

2019 ◽  
Vol 10 (2) ◽  
pp. 301-309
Author(s):  
A. Bharali ◽  
Amitav Doley
Keyword(s):  
Zagreb Index ◽  
Graph Operations

The Restricted Arc-Width of a Graph

10.37236/1734 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
David Arthur
Keyword(s):  
Unit Circle ◽  
Single Point ◽  
Minimum Width ◽  
Graph Operations ◽  
Function Mapping

An arc-representation of a graph is a function mapping each vertex in the graph to an arc on the unit circle in such a way that adjacent vertices are mapped to intersecting arcs. The width of such a representation is the maximum number of arcs passing through a single point. The arc-width of a graph is defined to be the minimum width over all of its arc-representations. We extend the work of Barát and Hajnal on this subject and develop a generalization we call restricted arc-width. Our main results revolve around using this to bound arc-width from below and to examine the effect of several graph operations on arc-width. In particular, we completely describe the effect of disjoint unions and wedge sums while providing tight bounds on the effect of cones.

Master Connectivity Index and Master Connectivity Polynomial

2010 ◽  
Vol 6 (4) ◽  
pp. 235-239
Author(s):  
Damir Vukicevic ◽  
Nenad Trinajstic ◽  
Sonja Nikolic ◽  
Bono Lucic ◽  
Bo Zhou
Keyword(s):  
Connectivity Index

The Sum-Connectivity Index - An Additive Variant of the Randic Connectivity Index§

2013 ◽  
Vol 9 (2) ◽  
pp. 184-194 ◽  
Author(s):  
Bono Lucic ◽  
Ivan Sovic ◽  
Jadranko Batista ◽  
Karolj Skala ◽  
Dejan Plavsic ◽  
...  
Keyword(s):  
Connectivity Index ◽  
Randić Connectivity Index
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