scholarly journals Extremal Trees with Respect to the Difference between Atom-Bond Connectivity Index and Randić Index

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1591
Author(s):  
Wan Nor Nabila Nadia Wan Zuki ◽  
Zhibin Du ◽  
Muhammad Kamran Jamil ◽  
Roslan Hasni
Keyword(s):  
Graph Theory ◽  
Connectivity Index ◽  
Randić Index ◽  
Extremal Graphs ◽  
Randic Index ◽  
Chemical Graph Theory ◽  
The Difference ◽  
Atom Bond ◽  
Chemical Trees

Let G be a simple, connected and undirected graph. The atom-bond connectivity index (ABC(G)) and Randić index (R(G)) are the two most well known topological indices. Recently, Ali and Du (2017) introduced the difference between atom-bond connectivity and Randić indices, denoted as ABC−R index. In this paper, we determine the fourth, the fifth and the sixth maximum chemical trees values of ABC−R for chemical trees, and characterize the corresponding extremal graphs. We also obtain an upper bound for ABC−R index of such trees with given number of pendant vertices. The role of symmetry has great importance in different areas of graph theory especially in chemical graph theory.

scholarly journals Ordering of alkane isomers by means of connectivity indices

2002 ◽  
Vol 67 (2) ◽  
pp. 87-97 ◽  
Author(s):  
Ivan Gutman ◽  
Dusica Vidovic ◽  
Anka Nedic
Keyword(s):  
Carbon Atom ◽  
Organic Molecule ◽  
Molecular Graph ◽  
Connectivity Index ◽  
Randić Index ◽  
Randic Index ◽  
Connectivity Indices ◽  
The Difference

The connectivity index of an organic molecule whose molecular graph is Gis defined as C(?)=?(?u?v)??where ?u is the degree of the vertex u in G, where the summation goes over all pairs of adjacent vertices of G and where ? is a pertinently chosen exponent. The usual value of ? is ?1/2, in which case ?=C(?1/2) is referred to as the Randic index. The ordering of isomeric alkanes according to ??follows the extent of branching of the carbon-atom skeleton. We now study the ordering of the constitutional isomers of alkanes with 6 through 10 carbon atoms with respect to C(?) for various values of the parameter ?. This ordering significantly depends on ?. The difference between the orderings with respect to ??and with respect to C(?) is measured by a function ??and the ?-dependence of ??was established.

scholarly journals Molecular description of carbon graphite and crystal cubic carbon structures

2017 ◽  
Vol 95 (6) ◽  
pp. 674-686 ◽  
Author(s):  
Abdul Qudair Baig ◽  
Muhammad Imran ◽  
Waqas Khalid ◽  
Muhammad Naeem
Keyword(s):  
Crystal Structure ◽  
Graph Theory ◽  
Chemical Structure ◽  
Molecular Graph ◽  
Vital Role ◽  
Connectivity Index ◽  
Chemical Graph Theory ◽  
Carbon Structures ◽  
Molecular Description ◽  
Atom Bond

Graph theory plays a vital role in modeling and designing any chemical structure or chemical network. Chemical graph theory helps in understanding the molecular structural properties of a molecular graph. The molecular graph consists of atoms called vertices and chemical bonds between atoms called edges. In this article, we study the chemical graphs of carbon graphite and crystal structure of cubic carbon. Moreover, we compute and give closed formulas of degree-based additive topological indices, mainly the first and second Zagreb indexes, general Randić index, atom bond connectivity index, geometric arithmetic index, fourth atom bond connectivity index, and fifth geometric arithmetic index of carbon graphite denoted by CG(m, n) for t levels, and crystal structure cubic carbon denoted for n levels.

scholarly journals Study of Hardness of Superhard Crystals by Topological Indices

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Xiujun Zhang ◽  
Muhammad Naeem ◽  
Abdul Qudair Baig ◽  
Manzoor Ahmad Zahid
Keyword(s):  
Molecular Structure ◽  
Chemical Structure ◽  
Topological Indices ◽  
Connectivity Index ◽  
Chemical Bonds ◽  
Randić Index ◽  
Total Resistance ◽  
Randic Index ◽  
Atom Bond

Topological indices give immense information about a molecular structure or chemical structure. The hardness of materials for the indentation can be defined microscopically as the total resistance and effect of chemical bonds in the respective materials. The aim of this paper is to study the hardness of some superhard B C x crystals by means of topological indices, specifically Randić index and atom-bond connectivity index.

scholarly journals Inequalities on the Generalized ABC Index

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1151
Author(s):  
Paul Bosch ◽  
Edil D. Molina ◽  
José M. Rodríguez ◽  
José M. Sigarreta
Keyword(s):  
Hölder Inequality ◽  
Connectivity Index ◽  
Randić Index ◽  
Randic Index ◽  
General Randić Index ◽  
Abc Index ◽  
General Randic Index ◽  
Atom Bond

In this work, we obtained new results relating the generalized atom-bond connectivity index with the general Randić index. Some of these inequalities for ABCα improved, when α=1/2, known results on the ABC index. Moreover, in order to obtain our results, we proved a kind of converse Hölder inequality, which is interesting on its own.

scholarly journals Some degree-based topological indices of caboxy-terminated dendritic macromolecule

2021 ◽  
Vol 44 (1) ◽  
pp. 165-172
Author(s):  
Yongsheng Rao ◽  
Ammarah Kanwal ◽  
Riffat Abbas ◽  
Saima Noureen ◽  
Asfand Fahad ◽  
...  
Keyword(s):  
Graph Theory ◽  
Chemical Properties ◽  
Biochemical Properties ◽  
Topological Indices ◽  
Connectivity Index ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Modern Era ◽  
Dendritic Macromolecule ◽  
Atom Bond

Abstract In the modern era of the chemical science, the chemical graph theory has contributed significantly to exploring the properties of the chemical compounds. Currently, the computation of the topological indices is one of the most active directions of the research in the area of the chemical graph theory. The main feature of the study of the topological indices is its its ability of predicting the various physio-chemical properties. In this article, we compute several degree-based topological indices for the caboxy-terminated dendritic macromolecule. We compute Harmonic index, atom-bond connectivity index, geometric arithmetic index, sum connectivity index, inverse sum index, symmetric division degree, and Zagreb indices for caboxy-terminated dendritic macromolecule. The obtained results have potential to predict biochemical properties such as viscosity, entropy, and boiling point.

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 The Atom-Bond Connectivity Index of Catacondensed Polyomino Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jinsong Chen ◽  
Jianping Liu ◽  
Qiaoliang Li
Keyword(s):  
Upper Bound ◽  
Connectivity Index ◽  
Zigzag Chain ◽  
Extremal Graphs ◽  
Degree Of A Vertex ◽  
Abc Index ◽  
Atom Bond

LetG=(V,E)be a graph. The atom-bond connectivity (ABC) index is defined as the sum of weights((du+dv−2)/dudv)1/2over all edgesuvofG, wheredudenotes the degree of a vertexuofG. In this paper, we give the atom-bond connectivity index of the zigzag chain polyomino graphs. Meanwhile, we obtain the sharp upper bound on the atom-bond connectivity index of catacondensed polyomino graphs withhsquares and determine the corresponding extremal graphs.

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