The rapid growth of graph theory has sparked interest among analysts, driven by its diverse applications in mathematical chemistry. Closed-form solutions enable rapid property prediction without expensive simulations. This study delves into the second type of dominating David-derived network, which play a vital role in pharmaceutical development, hardware engineering, and system administration. We examine the topological features of the network, calculating distance-based indices like eccentricity measures and the eccentricity based Zagreb indices. Our findings offer novel perspectives on the structural attributes of dominating David-derived network, highlighting their potential impact across various disciplines.
2025-07
European Journal of Pure and Applied Mathematics
(القضية : 2)
(الحجم : 18)
Stability and Maximum Independent Bond Set Polynomials of Painkiller Molecules Using Maximum Matching
Chemical graph theory establishes a connection between the properties of molecules
and their corresponding molecular graphs. A topological index is a graph invariant that characterizes
the graph’s structure and remains unaffected by graph automorphisms. In chemical
graph theory, degree-based topological indices are particularly significant, offering crucial insights
into the structural features of molecules. In this work, we introduce the maximum independent
bond set polynomial MIBSP(H; x, y), a powerful tool for deriving various degree-based topological
indices. We specifically apply MIBSP(H; x, y), to the chemical graphs of several painkiller
molecules, including Aspirin, Paracetamol, Caffeine, Ibuprofen, Phenacetin, and Salicylic acid. The
degree-based topological indices derived from these polynomials provide a deeper understanding
of the molecular structures and their potential applications in pharmaceutical research.
2025-05
European Journal of Pure and Applied Mathematics
(القضية : 1)
(الحجم : 18)
M-Polynomial and Degree-Based Topological Indices for Iterative Graphs
Iterative graph have several applications in social network analysis, optimization problems, machine learning, and game theory. Such graphs are also commonly used in chemistry,
physics, and mathematics. In this article, we derive the M-polynomial for the fractal growth patterns of benzene (F GBn, n ≥ 1), the Pythagoras tree (P Tn, n ≥ 1), and the benzene dendrimer
(DBn, n ≥ 2). Moreover, we compute some degree-based topological indices based on the Mpolynomials, such as the first Zagreb index, the second Zagreb index, the modified second Zagreb
index, the general Randi´c index, the harmonic index, the inverse sum index, and the symmetric
division degree index. Finally, we presented our work graphically and compared the sketches of
M-polynomials and degree-based topological indices.
2025-01
Ain Shams Engineering Journal
(القضية : 6)
(الحجم : 14)
Computation of multiplicative topological aspects of hex-derived networks
A chemical network is numerically represented by a topological index in chemical graph theory. As opposed to
its chemical representation, a topological descriptor correlates with specific physical properties of the underlying
chemical molecules. In this article, third type of hex-derived networks HDN3(r), THDN3(r), are described. The
goal of this study is to develop some updated and closed formulas based on multiplicative graph invariants.
Such as ordinary geometric-arithmetic (OGA), general version of harmonic index (GHI), sum connectivity index
(SI), general sum connectivity index (GSI), first and second Gourava and hyper-Gourava indices, Shegehalli
and Kanabur indices, first generalized version of Zagreb index (GZI), and forgotten index (FI) for the hexderived
HDN3(r), THDN3(r), networks. Moreover, various types of edge for computing have been discovered and
analyzed along with the order and size. The calculation of multiplicative topological features in networks that
are generated from hexagonal structures is the main task of this work. Gaining more insight into the structural
characteristics and possible uses of these networks requires examining the interaction between topological
aspects and multiplication processes. To interpret the chemical compounds’, physical and biological attributes,
we can integrate the analysis of the networks stated above with the chemical compounds and their graphical
structures. These results can be utilized to evaluate the biological and physio-chemical activities of compounds.
2024-03
Journal of Mathematical Chemistry
On topological indices of third type of hex-derived networks
A topological index is a numerical representation of a chemical network in chemical
graph theory. Similar to their chemical representation, a topological descriptor identifies specific the physical attributes of the underlying chemical compounds.We describe
the third type of hex-derived networks rectangular hex-derived network RHDN3,
chain hex-derived network CHDN3, in our work (r). In this paper, modified and
efficient formulas based on multiplicative graph invariants will be constructed. Such
as ordinary geometric-arithmetic (OGA), general version of harmonic index (GHI),
sum connectivity indes (SI), general sum connectivity index (GSI), first and second
Gourava and hyper- Gourava indices, Shegehalli and Kanabur indices, first generalised
version of Zagreb index (GZI) and forgotten index (FI) for the subdivided hex -derived
RHDN3(r), CHDN3(r) networks. In order to develop some new formulas we the
compute the multiplicative topological properties. This study found several types of
edges for computing and also discussed the order and size.To properly appreciate
the chemical compounds, physical and biological characteristics we can combine the
study of the networks described above with the chemical compounds and their graphical structures. These observations have the potential to evaluate bio and physiological
activities.
Dominating David-derived networks are widely studied due to their
fractal nature, with applications in topology, chemistry, and computer sciences. The use of
molecular structure descriptors is a standard procedure that is used to correlate the biological
activity of molecules with their chemical structures, which can be useful in the field of
pharmacology.
2023-09
Mathematical Problems in Engineering
Computation of Benzenoid Planar Octahedron Networks by Using Topological Indices
Chemical descriptors are numeric numbers that contain a basic chemical structure and describe the structure of a graph. A graph’s topological indices are linked to its chemical characteristics. Biological activity of chemical compounds can be predicted using topological indices. Numerous chemical indices have been developed in theoretical chemistry, including the Zagreb index, the Randić index, the Wiener index, and many others. In this paper, we compute the exact results for the Randić, Zagreb, Harmonic, augmented Zagreb, atom-bond connectivity, and geometric-arithmetic indices for the Benzenoid networks theoretically.
2023-04
Journal of Chemistry
Comparative Study of Prism Octahedron Network via Eccentric Invariants
Topological indices are empirical features of graphs that characterize the topology of the graph and, for the most part, are graph
independent. An important branch of graph theory is chemical graph theory. In chemical graph theory, the atoms corresponds
vertices and edges corresponds covalent bonds. A topological index is a numeric number that represents the topology of underline
structure. In this article, we examined the topological properties of prism octahedron network of dimension m and computed the
total eccentricity, average eccentricity, Zagreb eccentricity, geometric arithmetic eccentricity, and atom bond connectivity eccentricity indices, which are used to utilize the distance between the vertices of a prism octahedron network.
2023-03
Molecules
(القضية : 556)
(الحجم : 28)
Comparative Study of Planar Octahedron Molecular Structure via Eccentric Invariants
A branch of graph theory that makes use of a molecular graph is called chemical graph
theory. Chemical graph theory is used to depict a chemical molecule. A graph is connected if
there is an edge between every pair of vertices. A topological index is a numerical value related to
the chemical structure that claims to show a relationship between chemical structure and various
physicochemical attributes, chemical reactivity, or, you could say, biological activity. In this article, we
examined the topological properties of a planar octahedron network of m dimensions and computed
the total eccentricity, average eccentricity, Zagreb eccentricity, geometric arithmetic eccentricity, and
atom bond connectivity eccentricity indices, which are used to determine the distance between the
vertices of a planar octahedron network.
2023-01
Mathematical Biosciences and Engineering
(الحجم : 20)
Breast cancer chemical structures and their partition resolvability
Cancer is a disease that causes abnormal cell formation and spreads throughout the body,
causing harm to other organs. Breast cancer is the most common kind among many of cancers worldwide. Breast cancer affects women due to hormonal changes or genetic mutations in DNA. Breast
cancer is one of the primary causes of cancer worldwide and the second biggest cause of cancer-related
deaths in women. Metastasis development is primarily linked to mortality. Therefore, it is crucial for
public health that the mechanisms involved in metastasis formation are identified. Pollution and the
chemical environment are among the risk factors that are being indicated as impacting the signaling
pathways involved in the construction and growth of metastatic tumor cells. Due to the high risk of
mortality of breast cancer, breast cancer is potentially fatal, more research is required to tackle the
deadliest disease. We considered different drug structures as chemical graphs in this research and computed the partition dimension. This can help to understand the chemical structure of various cancer
drugs and develop formulation more efficiently.
2022-12
ARS Mathematica Contemporanea
(القضية : 18)
(الحجم : 16)
The Conductivity of Superimposed key-Graph with Common One-Dimensional Adjacency Nullspace
