Topological indices for molecular fragments and new graph invariants

1988 ◽  
Vol 2 (4) ◽  
pp. 347-375 ◽  
Author(s):  
Ovanes Mekenyan ◽  
Danail Bonchev ◽  
Alexandru Balaban
Keyword(s):  
Topological Indices ◽  
Molecular Fragments ◽  
Graph Invariants

New Topological Indices for Substituents (Molecular Fragments)

1994 ◽  
Vol 2 (1-2) ◽  
pp. 1-16 ◽  
Author(s):  
A. T. Balaban ◽  
C. Catana
Keyword(s):  
Topological Indices ◽  
Molecular Fragments

scholarly journals Topological Indices of Para-line Graphs of V-Phenylenic Nanostructures

2019 ◽  
Vol 17 (1) ◽  
pp. 260-266 ◽  
Author(s):  
Imran Nadeem ◽  
Hani Shaker ◽  
Muhammad Hussain ◽  
Asim Naseem
Keyword(s):  
Chemical Properties ◽  
Topological Indices ◽  
Structural Chemistry ◽  
Line Graphs ◽  
Physical And Chemical Properties ◽  
Graph Invariants ◽  
Molecular Graphs ◽  
Physical And Chemical ◽  
And Chemical Properties

Abstract The degree-based topological indices are numerical graph invariants which are used to correlate the physical and chemical properties of a molecule with its structure. Para-line graphs are used to represent the structures of molecules in another way and these representations are important in structural chemistry. In this article, we study certain well-known degree-based topological indices for the para-line graphs of V-Phenylenic 2D lattice, V-Phenylenic nanotube and nanotorus by using the symmetries of their molecular graphs.

A new approach for devising local graph invariants: Derived topological indices with low degeneracy and good correlation ability

1987 ◽  
Vol 1 (1) ◽  
pp. 61-83 ◽  
Author(s):  
P. A. Filip ◽  
T. -S. Balaban ◽  
A. T. Balaban
Keyword(s):  
Topological Indices ◽  
Graph Invariants ◽  
New Approach ◽  
Local Graph

Correlations using topological indices based on real graph invariants

1992 ◽  
Vol 89 ◽  
pp. 1735-1745 ◽  
Author(s):  
AT Balaban ◽  
TS Balaban
Keyword(s):  
Topological Indices ◽  
Graph Invariants

scholarly journals On Realization and Characterization of Topological Indices

2019 ◽  
Vol 9 (1) ◽  
pp. 715-718
Keyword(s):  
Topological Index ◽  
Fixed Number ◽  
Topological Indices ◽  
Molecular Structures ◽  
Real Numbers ◽  
Graph Invariants ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Chemical Graph Theory

In chemical graph theory, topological index is one of the graph invariants which is a fixed number based on structure of a graph. Topological index is used as one of the tool to analyze molecular structures and for proper and optimal design of nanostructure. In this paper we realize the real numbers that are topological indices such as Zagreb indices, Randic index, NK-index, multiplicative F-index and multiplicative Zagreb indices along with some characterizations.

On edge-degree based invariants of graphs

2021 ◽  
Author(s):  
Ali Reza Ashrafi ◽  
Ali Ghalavand
Keyword(s):  
Topological Indices ◽  
Graph Invariants ◽  
The Third

Let [Formula: see text] be a graph with edge set [Formula: see text]. For an edge [Formula: see text] in [Formula: see text], we define [Formula: see text], where [Formula: see text] and [Formula: see text] are degrees of vertices [Formula: see text] and [Formula: see text] in [Formula: see text], respectively. For [Formula: see text], the graph invariants [Formula: see text], [Formula: see text] and [Formula: see text] are defined as [Formula: see text], [Formula: see text] and [Formula: see text], where [Formula: see text] means that the edges [Formula: see text] and [Formula: see text] are incident. In this paper, some relationship between these graph invariants and some classical topological indices were presented. Moreover, some bounds for [Formula: see text], [Formula: see text] and [Formula: see text] are obtained and trees with the first through the third smallest [Formula: see text] and [Formula: see text], as well as the trees with the first through the forth smallest [Formula: see text] are also characterized.

scholarly journals On Face Index of Silicon Carbides

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Xiujun Zhang ◽  
Ali Raza ◽  
Asfand Fahad ◽  
Muhammad Kamran Jamil ◽  
Muhammad Anwar Chaudhry ◽  
...  
Keyword(s):  
Physical Properties ◽  
Computer Networks ◽  
Chemical Structure ◽  
Topological Indices ◽  
Graph Invariant ◽  
Graph Invariants ◽  
Chemical Structures ◽  
Boiling Points ◽  
Silicon Carbides ◽  
The Face

Several graph invariants have been defined and studied, which present applications in nanochemistry, computer networks, and other areas of science. One vastly studied class of the graph invariants is the class of the topological indices, which helps in the studies of chemical, biological, and physical properties of a chemical structure. One recently introduced graph invariant is the face index, which can assist in predicting the energy and the boiling points of the certain chemical structures. In this paper, we drive the analytical closed formulas of face index of silicon carbides Si2C3−Ia,b, Si2C3−IIa,b, Si2C3−IIIa,b, and SiC3−IIIa,b.

scholarly journals Relationships between some distance-based topological indices

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 5809-5815 ◽  
Author(s):  
Hongbo Hua ◽  
Ivan Gutman ◽  
Hongzhuan Wang ◽  
Kinkar Das
Keyword(s):  
Connected Graph ◽  
Average Distance ◽  
Topological Indices ◽  
Graph Invariants ◽  
Harary Index ◽  
Eccentricity Index ◽  
Polarity Index ◽  
The Relationship

The Harary index (HI), the average distance (AD), the Wiener polarity index (WPI) and the connective eccentricity index (CEI) are distance-based graph invariants, some of which found applications in chemistry. We investigate the relationship between HI, AD, and CEI, and between WPI, AD, and CEI. First, we prove that HI > AD for any connected graph and that HI > CEI for trees, with only three exceptions. We compare WPI with CEI for trees, and give a classification of trees for which CEI ? WPI or CEI < WPI. Furthermore, we prove that for trees, WPI > AD, with only three exceptions.

scholarly journals Some Vertex/Edge-Degree-Based Topological Indices of r -Apex Trees

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Akbar Ali ◽  
Waqas Iqbal ◽  
Zahid Raza ◽  
Ekram E. Ali ◽  
Jia-Bao Liu ◽  
...  
Keyword(s):  
Graph Theory ◽  
Connected Graph ◽  
Nonnegative Integer ◽  
Symmetric Function ◽  
Topological Indices ◽  
Vertex Degree ◽  
Graph Invariants ◽  
Arbitrary Vertex ◽  
Chemical Graph ◽  
Chemical Graph Theory

In chemical graph theory, graph invariants are usually referred to as topological indices. For a graph G , its vertex-degree-based topological indices of the form BID G = ∑ u v ∈ E G β d u , d v are known as bond incident degree indices, where E G is the edge set of G , d w denotes degree of an arbitrary vertex w of G , and β is a real-valued-symmetric function. Those BID indices for which β can be rewritten as a function of d u + d v − 2 (that is degree of the edge u v ) are known as edge-degree-based BID indices. A connected graph G is said to be r -apex tree if r is the smallest nonnegative integer for which there is a subset R of V G such that R = r and G − R is a tree. In this paper, we address the problem of determining graphs attaining the maximum or minimum value of an arbitrary BID index from the class of all r -apex trees of order n , where r and n are fixed integers satisfying the inequalities n − r ≥ 2 and r ≥ 1 .

Tetracyclic graphs with maximum second Zagreb index: A simple approach

2018 ◽  
Vol 11 (05) ◽  
pp. 1850064 ◽  
Author(s):  
Akbar Ali
Keyword(s):  
Graph Theory ◽  
Short Note ◽  
Topological Indices ◽  
Simple Approach ◽  
Graph Invariants ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Second Zagreb Index ◽  
Chemical Graph Theory

In the chemical graph theory, graph invariants are usually referred to as topological indices. The second Zagreb index (denoted by [Formula: see text]) is one of the most studied topological indices. For [Formula: see text], let [Formula: see text] be the collection of all non-isomorphic connected graphs with [Formula: see text] vertices and [Formula: see text] edges (such graphs are known as tetracyclic graphs). Recently, Habibi et al. [Extremal tetracyclic graphs with respect to the first and second Zagreb indices, Trans. on Combin. 5(4) (2016) 35–55.] characterized the graph having maximum [Formula: see text] value among all members of the collection [Formula: see text]. In this short note, an alternative but relatively simple approach is used for characterizing the aforementioned graph.

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