Inverse problem for Zagreb indices Yurtas, Aysun; Togan, Muge; Lokesha, Veerebradiah ...
Journal of mathematical chemistry,
15/2, Letnik:
57, Številka:
2
Journal Article
Recenzirano
The inverse problem for integer-valued topological indices is about the existence of a graph having its index value equal to a given integer. We solve this problem for the first and second Zagreb ...indices, and present analogous results also for the forgotten and hyper-Zagreb index. The first Zagreb index of connected graphs can take any even positive integer value, except 4 and 8. The same is true if one restricts to trees or to molecular graphs. The second Zagreb index of connected graphs can take any positive integer value, except 2, 3, 5, 6, 7, 10, 11, 13, 15 and 17. The same is true if one restricts to trees or to molecular graphs.
In this article, we study benzenoid Triangular system and benzenoid Hourglass system and we compute Zagreb polynomials for benzenoid Triangular system and benzenoid Hourglass system and from these ...Zagreb polynomials we catch up degree based Zagreb indices.
Let G be a graph with n vertices and d
i is the degree of its ith vertex (d
i is the degree of v
i). In this article, we compute the redefined first Zagreb index, redefined second Zagreb index, ...redefined third Zagreb index, augmented Zagreb index of graphs carbon nanocones CNC
kn, and nanotori C4C6C8(p,q). Also, compute the multiplicative redefined first Zagreb index, multiplicative redefined second Zagreb index, multiplicative redefined third Zagreb index, multiplicative augmented Zagreb index of carbon nanocones CNC
kn, and nanotori C4C6C8(p,q).
The molecular graph of nanocones have conical structures with a cycle of length k at its core and n layers of hexagons placed at the conical surface around its center, show carbon nanocones in this figure.
Beyond the Zagreb indices Gutman, Ivan; Milovanović, Emina; Milovanović, Igor
AKCE International Journal of Graphs and Combinatorics,
01/2020, Letnik:
17, Številka:
1
Journal Article
Recenzirano
Odprti dostop
The two Zagreb indices M1=∑vd(v)2 and M2=∑uvd(u)d(v) are vertex-degree-based graph invariants that have been introduced in the 1970s and extensively studied ever since. In the last few years, a ...variety of modifications of M1 and M2 were put forward. The present survey of these modified Zagreb indices outlines their main mathematical properties, and provides an exhaustive bibliography.
•Connection-based topological indices help represent the carbon nanotube structures in a concise mathematical form.•The calculated topological indices can be correlated with various properties of ...carbon nanotubes.•Topological indices can shed light on the reactivity and chemical behavior of carbon nanotubes.•Different carbon nanotubes exhibit distinct topological characteristics, such as chirality and diameter.•Study of topological indices and nanotube properties relationship shows how structural features influence materials’ behavior / performance.
Topological indices (TIs) are mathematical codings of the molecular graphs that predict the physicochemical, biological, toxicological, and structural properties of the chemical compounds. To evaluate the physical and chemical properties of molecules, numerous TIs have been studied in the literature. In chemical research, a nanostructure is one of the most important and frequently studied substances. It was created using molecular-scale engineering mechanisms. Zagreb indices (ZIs) are the majority studied by TIs. TIs are categorized based on their degree, distance, and polynomial. Connection-based topological indices (ZCIs), one of these TIs, are extremely important. In this article, we compute several connection-based topological indices for carbon nanotube graphs. We obtain first ZCI (1st ZCI) and second ZCI (2nd ZCI) and modified first ZCI (1*st ZCI), modified second ZCI (2*nd ZCI), modified third ZCI (3*rd ZCI), and modified fourth ZCI (4*th ZCI). Moreover, we compute multiplicative ZCI (MZCI), named as first MZCI (1st MZCI), second MZCI (2nd MZCI), third MZCI (3rd MZCI), fourth MZCI (4th MZCI), and modified first (1*st MZCI), modified second (2*nd MZCI), and modified third (3*rd MZCI) for carbon nanotube graphs.
Metal–organic frameworks (MOFs) are intriguing porous materials that are formed by combining organic materials with metals. MOFs have a vast range of utilizations in distinct medical fields with ...great efficiency. Recently, Zinc-related MOFs have been investigated and are in demand due to their efficient utilization in medical fields such as biosensing, cancer therapy and drug delivery. To mathematically characterize the chemical structures using numerical graph descriptors is the present-day line of research. A numerical graph descriptor or a topological index (TI) is a numerical quantity that is linked with graphs and assists in correlating the topology of a chemical compound. Various distance-based descriptors can be found in the literature. Connection-based TIs, instead of degree-based TIs are considered to be more potent in measuring the chemical aspects of molecular compounds. In this paper, we compute the connection-based TIs of zinc-related MOFs such as zinc oxide and zinc silicate. Further, to examine superiority, we numerically and graphically compare these zinc-related MOFS with each other on the basis of their computed results.
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For a graph
G
=
(
V
(
G
)
,
E
(
G
)
)
, let
d
(
u
),
d
(
v
) be the degrees of the vertices
u
,
v
in
G
. The first and second Zagreb indices of
G
are defined as
M
1
(
G
)
=
∑
u
∈
V
(
G
)
d
(
u
)
2
...and
M
2
(
G
)
=
∑
u
v
∈
E
(
G
)
d
(
u
)
d
(
v
)
, respectively. The first (generalized) and second Multiplicative Zagreb indices of
G
are defined as
Π
1
,
c
(
G
)
=
∏
v
∈
V
(
G
)
d
(
v
)
c
and
Π
2
(
G
)
=
Π
u
v
∈
E
(
G
)
d
(
u
)
d
(
v
)
, respectively. The (Multiplicative) Zagreb indices have been the focus of considerable research in computational chemistry dating back to Narumi and Katayama in 1980s. Denote by
G
n
the set of all Eulerian graphs of order
n
. In this paper, we characterize Eulerian graphs with first three smallest and largest Zagreb indices and Multiplicative Zagreb indices in
G
n
.
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