On equitable chromatic topological indices of some Mycielski graphs

2021 ◽  
Vol 29 (2) ◽  
pp. 221-229
Author(s):  
SMITHA ROSE ◽  
SUDEV NADUVATH
Keyword(s):  
Topological Indices ◽  
Proper Coloring ◽  
Zagreb Indices ◽  
Equitable Coloring ◽  
Graph Classes ◽  
Basic Graph ◽  
Special Classes

In recent years, the notion of chromatic Zagreb indices has been introduced and studied for certain basic graph classes, as a coloring parallel of different Zagreb indices. A proper coloring C of a graph G, which assigns colors to the vertices of G such that the numbers of vertices in any two color classes differ by at most one, is called an equitable coloring of G. In this paper, we introduce the equitable chromatic Zagreb indices and equitable chromatic irregularity indices of some special classes of graphs called Mycielski graphs of paths and cycles.

Equitable coloring parameters of certain graph classes

2018 ◽  
Vol 10 (03) ◽  
pp. 1850040
Author(s):  
Sudev Naduvath
Keyword(s):  
Random Variable ◽  
Mass Function ◽  
Probability Mass Function ◽  
Proper Coloring ◽  
Discrete Random Variable ◽  
Statistical Parameters ◽  
Equitable Coloring ◽  
Graph Classes ◽  
Probability Mass ◽  
The Given

Coloring the vertices of a graph [Formula: see text] subject to given conditions can be considered as a random experiment and corresponding to this experiment, a discrete random variable [Formula: see text] can be defined as the color of a vertex chosen at random, with respect to the given type of coloring of [Formula: see text] and a probability mass function for this random variable can be defined accordingly. A proper coloring [Formula: see text] of a graph [Formula: see text], which assigns colors to the vertices of [Formula: see text] such that the numbers of vertices in any two color classes differ by at most one, is called an equitable coloring of [Formula: see text]. In this paper, we study two statistical parameters of certain graphs, with respect to their equitable colorings.

scholarly journals Mathematical Properties of Variable Topological Indices

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 43
Author(s):  
José M. Sigarreta
Keyword(s):  
Real Number ◽  
Large Class ◽  
Symmetric Functions ◽  
Topological Indices ◽  
Current Interest ◽  
Zagreb Indices ◽  
Mathematical Properties ◽  
Connectivity Indices ◽  
Optimal Bounds ◽  
New Framework

A topic of current interest in the study of topological indices is to find relations between some index and one or several relevant parameters and/or other indices. In this paper we study two general topological indices Aα and Bα, defined for each graph H=(V(H),E(H)) by Aα(H)=∑ij∈E(H)f(di,dj)α and Bα(H)=∑i∈V(H)h(di)α, where di denotes the degree of the vertex i and α is any real number. Many important topological indices can be obtained from Aα and Bα by choosing appropriate symmetric functions and values of α. This new framework provides new tools that allow to obtain in a unified way inequalities involving many different topological indices. In particular, we obtain new optimal bounds on the variable Zagreb indices, the variable sum-connectivity index, the variable geometric-arithmetic index and the variable inverse sum indeg index. Thus, our approach provides both new tools for the study of topological indices and new bounds for a large class of topological indices. We obtain several optimal bounds of Aα (respectively, Bα) involving Aβ (respectively, Bβ). Moreover, we provide several bounds of the variable geometric-arithmetic index in terms of the variable inverse sum indeg index, and two bounds of the variable inverse sum indeg index in terms of the variable second Zagreb and the variable sum-connectivity indices.

scholarly journals On the Multiplicative Degree-Based Topological Indices of Silicon-Carbon Si2C3-I[p,q] and Si2C3-II[p,q]

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 320 ◽  
Author(s):  
Young Kwun ◽  
Abaid Virk ◽  
Waqas Nazeer ◽  
M. Rehman ◽  
Shin Kang
Keyword(s):  
Molecular Structure ◽  
Graph Theory ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Topological Indices ◽  
Molecular Compound ◽  
Zagreb Indices ◽  
Silicon Carbon ◽  
Physico Chemical ◽  
Structure Research

The application of graph theory in chemical and molecular structure research has far exceeded people’s expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonds by edges. Topological indices help us to predict many physico-chemical properties of the concerned molecular compound. In this article, we compute Generalized first and multiplicative Zagreb indices, the multiplicative version of the atomic bond connectivity index, and the Generalized multiplicative Geometric Arithmetic index for silicon-carbon Si2C3−I[p,q] and Si2C3−II[p,q] second.

scholarly journals Computation of Zagreb and atom-bond connectivity indices of certain families of dendrimers by using automorphism group action

2017 ◽  
Vol 82 (2) ◽  
pp. 151-162
Author(s):  
Uzma Ahmad ◽  
Sarfraz Ahmad ◽  
Rabia Yousaf
Keyword(s):  
Automorphism Group ◽  
Carbon Atom ◽  
Physicochemical Properties ◽  
Group Action ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Zagreb Indices ◽  
Connectivity Indices ◽  
Atom Bond

In QSAR/QSPR studies, topological indices are utilized to predict the bioactivity of chemical compounds. In this paper, the closed forms of different Zagreb indices and atom?bond connectivity indices of regular dendrimers G[n] and H[n] in terms of a given parameter n are determined by using the automorphism group action. It was reported that these connectivity indices are correlated with some physicochemical properties and are used to measure the level of branching of the molecular carbon-atom skeleton.

scholarly journals Zagreb Polynomials and redefined Zagreb indices of nanostar dendrimers

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 31-40 ◽  
Author(s):  
Shin Min Kang ◽  
Muhammad Yousaf ◽  
Manzoor Ahmad Zahid ◽  
Muhammad Younas ◽  
Waqas Nazeer
Keyword(s):  
Boiling Point ◽  
Strain Energy ◽  
Chemical Properties ◽  
Topological Indices ◽  
Central Core ◽  
Zagreb Indices ◽  
Physico Chemical

Abstract Dendrimers are profoundly extended natural macromolecules with successive layers of branch units encompassing a central core. Topological indicess are numbers related with graph of a compound to allow quantitative structureactivity/property/lethality connections. These topological indices relate certain physico-chemical properties like stability, boiling point, strain energy and so forth of a compound. In this report, there have been computed redefined first, second and third Zagreb indices of Nanostar dendrimers. The authors also analyzed some Zagreb polynomials of understudy dendrimers.

scholarly journals Valency-based molecular descriptors of Bakelite network BNmn$B\text N_{m}^{n}$

2019 ◽  
Vol 17 (1) ◽  
pp. 663-670 ◽  
Author(s):  
Maqsood Ahmad ◽  
Muhammad Javaid ◽  
Muhammad Saeed ◽  
Chahn Yong Jung
Keyword(s):  
Physical Properties ◽  
Molecular Descriptors ◽  
Molecular Graph ◽  
Synthetic Polymer ◽  
Topological Indices ◽  
Qsar Studies ◽  
Zagreb Indices ◽  
Symmetric Division ◽  
Atom Bond

AbstractBakelite network $BN_{m}^{n}$is a molecular graph of bakelite, a pioneering and revolutionary synthetic polymer (Thermosetting Plastic) and regarded as the material of a thousand uses. In this paper, we aim to compute various degree-based topological indices of a molecular graph of bakelite network $BN_{m}^{n}$. These molecular descriptors play a fundamental role in QSPR/QSAR studies in describing the chemical and physical properties of Bakelite network $BN_{m}^{n}$. We computed atom-bond connectivity ABC its fourth version ABC4 geometric arithmetic GA its fifth version GA5 Narumi-Katayama, sum-connectivity and Sanskruti indices, first, second, modified and augmented Zagreb indices, inverse and general Randic’ indices, symmetric division, harmonic and inverse sum indices of $BN_{m}^{n}$.

On degree-based topological descriptors of strong product graphs

2016 ◽  
Vol 94 (6) ◽  
pp. 559-565 ◽  
Author(s):  
Shehnaz Akhter ◽  
Muhammad Imran
Keyword(s):  
Physicochemical Properties ◽  
Strain Energy ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Topological Descriptors ◽  
Zagreb Indices ◽  
Strong Product ◽  
Product Graphs ◽  
Product Of Graphs ◽  
Atom Bond

Topological descriptors are numerical parameters of a graph that characterize its topology and are usually graph invariant. In a QSAR/QSPR study, physicochemical properties and topological indices such as Randić, atom–bond connectivity, and geometric–arithmetic are used to predict the bioactivity of different chemical compounds. There are certain types of topological descriptors such as degree-based topological indices, distance-based topological indices, counting-related topological indices, etc. Among degree-based topological indices, the so-called atom–bond connectivity and geometric–arithmetic are of vital importance. These topological indices correlate certain physicochemical properties such as boiling point, stability, strain energy, etc., of chemical compounds. In this paper, analytical closed formulas for Zagreb indices, multiplicative Zagreb indices, harmonic index, and sum-connectivity index of the strong product of graphs are determined.

scholarly journals On Leap Reduced Reciprocal Randic and Leap Reduced Second Zagreb Indices of Some Graphs

2019 ◽  
Vol 3 (2) ◽  
pp. 27-35
Author(s):  
Fazal Dayan ◽  
Muhammad Javaid ◽  
Muhammad Aziz ur Rehman
Keyword(s):  
Topological Indices ◽  
Randić Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Zagreb Indices ◽  
Second Zagreb Index ◽  
Second Degree

Naji et al. introduced the leap Zagreb indices of a graph in 2017 which are new distance-degree-based topological indices conceived depending on the second degree of vertices. In this paper, we have defined the first and second leap reduced reciprocal Randic index and leap reduced second Zagreb index for selected wheel related graphs.

scholarly journals Certain topological indices and polynomials for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph

2020 ◽  
Vol 3 (2) ◽  
pp. 63
Author(s):  
Salma Kanwal ◽  
Mariam Imtiaz ◽  
Ayesha Manzoor ◽  
Nazeeran Idrees ◽  
Ammara Afzal
Keyword(s):  
Line Graph ◽  
Topological Indices ◽  
Point Graph ◽  
Zagreb Index ◽  
Harmonic Index ◽  
Zagreb Indices ◽  
Symmetric Division ◽  
Augmented Zagreb Index ◽  
Forgotten Index

<p>Dutch windmill graph [1, 2] and denoted by <em>Dnm</em>. Order and size of Dutch windmill graph are (<em>n</em>−1)<em>m</em>+1 and mn respectively. In this paper, we computed certain topological indices and polynomials i.e. Zagreb polynomials, hyper Zagreb, Redefined Zagreb indices, modified first Zagreb, Reduced second Zagreb, Reduced Reciprocal Randi´c, 1st Gourava index, 2nd Gourava index, 1st hyper Gourava index, 2nd hyper Gourava index, Product connectivity Gourava index, Sum connectivity Gourava index, Forgotten index, Forgotten polynomials, <em>M</em>-polynomials and some topological indices in term of the <em>M</em>-polynomials i.e. 1st Zagreb index, 2nd Zagreb index, Modified 2nd Zagreb, Randi´c index, Reciprocal Randi´c index, Symmetric division, Harmonic index, Inverse Sum index, Augmented Zagreb index for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph.</p>

scholarly journals On Multiple Zagreb Indices of Dendrimer Nanostars

2015 ◽  
Vol 52 ◽  
pp. 147-151 ◽  
Author(s):  
Mohammad Reza Farahani
Keyword(s):  
Topological Indices ◽  
Infinite Class ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Degree Of A Vertex

In this paper, we focus on the structure of an infinite class of Dendrimer Nanostars D3[n] (n≥0 is infinite integer) and counting its First Multiple Zagreb index and Second Multiple Zagreb index. The Multiple Zagreb topological indices are equal to PM1(G)=(dv+dv) and PM2(G)=(dv×dv), where dv is the degree of a vertex v.

Sign in / Sign up

Export Citation Format

Share Document