The various topological indices are helpful in predicting the bioactivity of molecular compounds in quantitative structure–activity relationship/quantitative structure–property relationship study. ...The Balaban index and Harary index are the distance-based indices. The sum-Balaban index is another variant of Balaban index. Harary index can be used to indicate the decay of interaction between any two atoms of molecules. Whereas, the Balaban and sum-Balaban indices can be linked with some physico-chemical properties of octanes and lower benzenoids. In this work, the closed expression of Balaban index, sum-Balaban index, and Harary index of some regular dendrimers in the form of parameter
are computed using the action of automorphism group of these dendrimers.
In this paper we consider graphs of order n with minimum Balaban index. Although the index was introduced 30 years ago, its minimum value and corresponding extremal graphs are still unknown, and it ...is unlikely that they can be precisely determined soon due to the mathematical intractability of the index. We show that this value is of order Θ(n−1). For small values of n we determine the extremal graphs and we observe that they are similar to dumbbell graphs. We find out that in the class of balanced dumbbell graphs those with clique sizes π/24n+o(n) and the path length n−o(n) have asymptotically the smallest value. We study dumbbell-like graphs in more detail, and we propose several conjectures regarding the structure of the extremal graphs.
On the Balaban Index of Chain Graphs Das, Kinkar Chandra
Bulletin of the Malaysian Mathematical Sciences Society,
07/2021, Letnik:
44, Številka:
4
Journal Article
Recenzirano
The Balaban index and sum-Balaban index of a connected (molecular) graph
G
are defined as
J
(
G
)
=
m
μ
+
1
∑
u
v
∈
E
(
G
)
1
σ
G
(
u
)
σ
G
(
v
)
and
S
J
(
G
)
=
m
μ
+
1
∑
u
v
∈
E
(
G
)
1
σ
G
(
u
)
+
...σ
G
(
v
)
,
respectively, where
m
is the number of edges,
μ
is the cyclomatic number,
σ
G
(
u
)
is the sum of distances between vertex
u
and all other vertices of
G
. In this paper, we establish that
K
D
S
(
n
-
3
,
1
)
>
K
D
S
(
n
-
4
,
2
)
>
⋯
>
K
D
S
n
2
-
1
,
n
2
-
1
(
K
=
J
,
S
J
)
,
where
D
S
(
p
,
q
)
is a double star on
n
(
=
p
+
q
+
2
,
p
≥
q
)
vertices. As an application, we determine the extremal graphs of the Balaban index and the sum-Balaban index in the class of chain graphs
G
on
n
vertices, where
G
is a tree or a unicyclic graph. Finally, we give an open problem on Balaban (sum-Balaban) index of connected chain graphs.
Abstract This paper explores the complex interplay between topological indices and structural patterns in networks of iron telluride ( FeTe ). We want to analyses and characterize the distinct ...topological features of ( FeTe ) by utilizing an extensive set of topological indices. We investigate the relationship that these indicators have with the network’s physical characteristics by employing sophisticated statistical techniques and curve fitting models. Our results show important trends that contribute to our knowledge of the architecture of the ( FeTe ) network and shed light on its physiochemical properties. This study advances the area of material science by providing a solid foundation for using topological indices to predict and analyses the behavior of intricate network systems. More preciously, we study the topological indices of iron telluride networks, an artificial substance widely used with unique properties due to its crystal structure. We construct a series of topological indices for iron telluride networks with exact mathematical analysis and determine their distributions and correlations using statistical methods. Our results reveal significant patterns and trends in the network structure when the number of constituent atoms increases. These results shed new light on the fundamental factors that influence material behavior, thus offering a deeper understanding of the iron telluride network and may contribute to future research and engineering of these materials.
In this article we discuss the reverse degree based topological indices for planar metal-organic networks like transition metal (TM) of the three-dimensional series such as: Ti, V, Cr,
or Zn, ...phthalocyanine, and tetracyanobenzene (TCNB) as free-standing sheets. In distinction, the TM-TCNB networks are metallic at least in one revolutionary orientation and demonstrate long-range ferromagnetic connect in case for magnetic erection, which illustrate ideal entrant and a stimulating prospect of unequaled applications in spintronics. Topological indices are numerical variables of a graph which describe its topology and are usually graph invariant. We have computed the reverse degree based topological indices like the reverse general Randic index, the reverse Balaban index, the reverse atom bond connectivity index, the reverse geometric index, the reverse Zagreb type indices, and the reverse augmented Zagreb index for this metal-organic networks TM-TCNB.
The molecular structure of hydroxychloroquine (HCQ) used in the treatment of malaria is recently suggested for emergency used in COVID-19. The chemical compound of HCQ is produced by chemical ...alteration of ethylene oxide from human products, such as waxy maize starch. The molecular graph is a graph comprising of atoms called vertices and the chemical bond between molecules is called edges. A topological index is a numerical representation of a chemical structure which correlates certain physico-chemical characteristics of underlying chemical compounds besides its numerical representation. To distinguish the creation of entropy-based measures from the structure of chemical graphs, several graph properties have been utilized. For computing the structural information of chemical graphs, the graph entropies have become the information-theoretic quantities. The graph entropy measure has attracted the research community due to its potential application in discrete mathematics, biology, and chemistry. In this paper, our contribution is to explore graph entropies for molecular structure of HCQ based on novel information function, which is the number of different degree vertices along with the number of edges between various degree vertices. More precisely, we have explored the degree-based topological characteristics of hydroxyethyl starch conjugated with hydroxychloroquine (HCQ-HEC). Also, we computed entropies of this structure by making a relation of degree-based topological indices with the help of information function. Moreover, we presented the numerical and graphical comparison of the computed results.
On the minimum value of sum-Balaban index Knor, Martin; Kranjc, Jaka; Škrekovski, Riste ...
Applied mathematics and computation,
06/2017, Letnik:
303
Journal Article
Recenzirano
Odprti dostop
We consider extremal values of sum-Balaban index among graphs on n vertices. We determine that the upper bound for the minimum value of the sum-Balaban index is at most 4.47934 when n goes to ...infinity. For small values of n we determine the extremal graphs and we observe that they are similar to dumbbell graphs, in most cases having one extra edge added to the corresponding extreme for the usual Balaban index. We show that in the class of balanced dumbbell graphs, those with clique sizes 2log(1+2)4n+o(n) have asymptotically the smallest value of sum-Balaban index. We pose several conjectures and problems regarding this topic.
In chemical graph theory, a topological index is a numerical representation of a chemical structure while a topological descriptor correlates certain physico-chemical characteristics of underlying ...chemical compounds besides its numerical representation. Graph theory plays an important role in modeling and designing any chemical network. A large number of properties like physico-chemical properties, thermodynamic properties, chemical activity and biological activity are determined by the chemical applications of graph theory. These properties can be characterized by certain graph invariants referred to as topological indices. In this paper, we discuss the titania nanotube
titania nanotube
and computed exact results for degree based topological indices.
Topological indices are the atomic descriptors that portray the structures of chemical compounds and they help us to anticipate certain physico-compound properties like boiling point, enthalpy of ...vaporization and steadiness. These properties can be described by certain graph invariants alluded to as topological indices. In this paper, we have computed topological indices of Para-line graph for honeycomb and graphene systems.
Dendrimers achieved great consideration in gene and drug delivery applications because of having highly administrable architecture. Unambiguous structure of dendrimers might reduce the ...unpredictability related to the molecule’s shape and size, and also boost the accuracy of drug delivery. Dendrimers have exclusive physical and chemical properties due to which they have extensive range of potential applications like chemical sensors, light harvesting material, enhance the solubility, antitumer therapy, medical diagnostics, drug delivery system, catalysts, and many more. With the total π-electron energy, the degree-based topological indices have a lot of iterations.
In this paper, our desideration is to compute the topological aspects of degree based entropy for fractal and cayley tree type dendrimers. More preciously, we explore two tree type dendrimers denoted by Fr ant Cm,n. Moreover, entropies are estimated of these two structures by generating a correlation between degree based topological indices and their entropies.
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