Browsing by Author "Prof. Dr. Muhammad Hussain"

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Degree Based Topological Invariants of Chemical Networks
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Fakhra Majid; FA23-RMT-009; Prof. Dr. Muhammad Hussain; LHR TP 9757
This thesis presents a comprehensive study of topological indices derived from graph theory, with a specific focus on the HourGlass System Carbon Nano Cone structures. By modeling these nano-scale carbon frameworks as simple, connected molecular graphs, we investigate a wide range of vertex degree-based and vertex neighborhood degree-based topological indices. The work explores indices such as the General Randic, General Inverse Randic, General Sombor, Harmonic, Geometric-Arithmetic, Hyper-Zagreb, Atomic Bond Connectivity, and numerous Kulli-Basava variants. These indices are computed analytically for HourGlass System Carbon Nano Cone configurations with both odd and even cycle lengths across varying dimensions. The results highlight the structural uniqueness and potential chemical properties of these networks, offering valuable insights for applications in nanotechnology, drug design, and chemical compound analysis. This research contributes to the advancement of chemical graph theory by establishing new mathematical formulations and expanding the predictive power of topological descriptors in nano-material science.
Distance based Topological Indices based on Line Graph of Different Chemical and Non-Chemical Graphs
(Library Information Services COMSATS University Lahore Campus, 2023-03-13) Sheeza Mahmood; LHR TP 8715; SP22-RMT-008; Prof. Dr. Muhammad Hussain
I Sheeza Mahmood, CIIT/SP22-RMT-008/LHR, hereby state that my MS thesis titled “Dis tance based Topological Indices based on Line Graph of Different Chemical and Non Chemical Graphs ” is my own work and has not been submitted previously by me for taking any degree from this University ”COMSATS University Islamabad, Lahore Cam pus” or anywhere else in the country/world. At any time if my statement is found to be incorrect even after my Graduate the university has the right to withdraw my MS degree.
Eccentricity based Topological Indices on Associated Line Graphs of Different Chemical Networks
(Library Information Services COMSATS University Lahore Campus, 2023-03-13) Jamila Faryal; SP22-RMT-002; Prof. Dr. Muhammad Hussain; LHR TP 8711
Graph theory acts as an essential tool in various fields and applications because of its versatility in modeling and solving problems involving relationships and connections. In this thesis, our aim is to compute the eccentricity based topological indices like to tal eccentricity, Zagreb indices, average eccentricity, Geometric Arithmetic index GA, atom-bond connectivity ABC index for the line graphs of first type of Hex-Derived Networks HDN1(s) as well as some other chemical structures. Furthermore, the basic topologies of these networks are also derived. We obtained their respective indices based on the categorization of the chemical graphs. These newly obtained indices give insight into the chemical and physical properties of molecules. This analysis will assist researchers engaged in the field of network sciences by clarifying the structure of the aforementioned networks. Moreover, the results presented in this thesis might offer ad vantages in predicting supplementary chemical, physical and structural characteristics of the molecular graphs being studied.
Graph Energies of Generalized Chain on Petersen Graphs
(Library Information Services, CUI Lahorez v, 2023) Adnan Ahmad; CIIT/FA21-RMT-037/LHR; Prof. Dr. Muhammad Hussain
. The upper and lower bound of graph energy with minimal and maximal energy is abroad ﬁeld of Spectral Graph theory. The energy of Graph E(G) in term of vertices and number of edges in graph G is involved in absolute value of eigen value adjacency matrix of G where l is the spectral radius. The Graph has energy equal toFinally, we determine the energy, pattern and irregularities of chain like Petersen Graph. Our exploring outputs will rely upon Size and Order of Graph, Degree of Graph, Irregular Graph, Multi Graph, Cyclic Graph, Bridge Graph, Connected and Planarity Graph, and Concept of Distance and Degree in Graph.We will construct linear functionals obtained from the differences of integral inequalities involving multidimensional monotone func- tions and give the log-convexity of these functionals using classical log-convexity method by cosidering a family of convex functions. At the end we will formulate Cauchy means for these functionals, using as an application of mean value theorems of Langrange and Cauchy type and deduce their monotonicity.
Mathematical Study of Topological Indices
(Library Information Services, CUI Lahore, 2022) Nida-Ul-Nasar; FA21-RMT-033; Prof. Dr. Muhammad Hussain
Metric Dimension on Line Graph of Different Chemical Structures
(Library Information Services COMSATS University Lahore Campus, 2024-03-17) Zunaira Ijaz; FA22-RMT-028; Prof. Dr. Muhammad Hussain; LHR TP 9387
The Metric Dimension of a graph G is the minimum number of basis element in a resolving set. Let G = (V,E) be a connected graph and length of a shortest path between u and v is known as distance, denoted by d(u, v) in G. Let B = b1,b2,...,bk be an ordered set of vertices of G. The representation r(u|B) of u with respect to B is the k tuple (d(u,b1),d(u,b2),d(u,b3),...,d(u,bk), where B is called a resolving set or locating set if every vertex of G is uniquely identified by its distances from the vertices of B or equivalently if distinct vertices of G have distinct representations with respect to B. A resolving set of minimum cardinality is called a basis for G and cardinality is the metric dimension of G is denoted by dim(G). We investigated metric dimension on Line Graph of Polythiophene Network, Backbone Network, Hex-derive Network and Chain Sillicate Networ
Statistical Analysis of some Chemical Network with respect to Several Topological Indices
(Library Information Services COMSATS University Lahore Campus, 2024-03-14) Fakhra Younas; FA22-RMT-036; Prof. Dr. Muhammad Hussain; LHR TP 9357
Statistical Analysis of some Chemical Network with respect to Several Topological Indices
Topological Indices Based on Line Graph of Different Chemical and Non Chemical Structures
(Library Information Services COMSATS University Lahore Campus, 2024-03-18) Sehrish Aslam; SP23-RMT-037; Prof. Dr. Muhammad Hussain; LHR TP 9572
The utilization of graph theory has expanded considerably across various disciplines, with notable advancements in chemical graph theory. In recent years, researchers have explored numerous innovative avenues within this field. A chemical graph models a molecule by representing atoms as vertices and chemical bonds as edges. Analyzing topological indices, which are mathematical measures of a molecule’s structure, is crucial for understanding its physical and chemical properties. Firstly, we focused on degree-based topological indices, namely the Randic index, atom bond connectivity index, geometric arithmetic index, the first and the second Zagreb indices and co-indices, hyper Zagreb index, Hyper Zagreb index of Subdivision graph and Line graph of Niobium Dioxide NbO2.
Topological Indices on Line Graph of Different Chemical Structures
(Library Information Services, CUI Lahore, 2023) FA21-RMT-003; Minahil ijaz; Prof. Dr. Muhammad Hussain
A topological index is a numerical measure that characterizes certain inherent properties or features (boiling point, stability and melting point, heat of creation and freezing point, and so on) of a Molecular graph representing some chemical compounds. These indices deﬁne topology and typically hold Graph invariant mathematical characteristics. The term ”molecular descriptor” refers to the process of turning chemical data from chemical com- pounds into meaningful numerical values. These molecular descriptors are commonly used in the investigation of quantitative structure-activity connections that provide insight on animated effects based on chemical structures. This study aims to investigate topological indices based on degrees, including Randic index, Sum connectivity index, Harmonic in- dex, First Zagreb, second zagreb and third zagreb indices, Augmented zagreb index, Hyper zagreb index, Atom bond connectivity index (ABC), Geometric arithmetic index (GA), In- verse sum indeg index (ISI) and The fourth iteration of the Atom bond connectivity index, the ﬁfth iteration of the Geometric arithmetic index, and the Sanskruti index for line graph of Polythiophene Network.
Topological Indices on Line Graphs of Different Chemical Network
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Aqsa Nazar; FA23-RMT-005; Prof. Dr. Muhammad Hussain; LHR TP 9753
This thesis investigates the structural and mathematical properties of the line graph of the HourGlass System Carbon Nano Cone using a wide range of topological indices derived from graph theory. Topological indices are numerical parameters that encapsulate the structural characteristics of a graph and have proven valuable in chemical graph theory for predicting the physicochemical properties of molecular compounds. The study focuses on two primary classes of indices: those based on vertex degree and those based on vertex neighborhood degree. A total of fifty vertex degree based and ninety vertex neighborhood degree-based indices are computed and analyzed for both even and odd cycle lengths of HGSCNC graphs. These include classical indices such as the Randic, Zagreb, and Atom-Bond Connectivity indices, as well as more recent and refined descriptors like the Generalized Somber Index, Hyper Zagreb Indices, Geometric-Arithmetic Index, and several Kulli–Basava variants. The HourGlass System Carbon Nano Cone is modeled as a finite, simple, undirected graph, satisfying all necessary conditions for the application of these indices. The results provide explicit analytical expressions and demonstrate the effectiveness of these indices in capturing the molecular complexity and connectivity of the HGSCNC structure. This work not only broadens the understanding of graph-theoretical modeling in nanostructures but also reinforces the applicability of topological indices in materials science, nanotechnology, and quantitative structure property relationship (QSPR) studies.
Topological Indices on Subdivided Graphs of Different Chemical Networks
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Hadiqa Malik; FA23-RMT-011; Prof. Dr. Muhammad Hussain; LHR TP 9759
This thesis offers a thorough analysis of topological indices derived from graph theory, with a specific focus on the Subdivided Chain Silicates and Honeycomb Networks. We explore a broad range of vertex degree and vertex neighborhood degree sum topological indices. The work explores indexes such as the Randic, General Randic, General Inverse Randic, Sombor, General Sombor, Harmonic, Geometric-Arithmetic, Hyper-Zagreb, Re-defined Zagreb, Augmented Zagreb, Atomic-bond Connectivity, Gourava and Hyper-Gourava, Symmetric Division Degree and numerous Kulli-Basava variants. These indices are computed analytically for subdivided chain silicates and honeycomb networks configurations with n-dimensions. These results demonstrate the structural distinctiveness and possible chemical characteristics of these networks, providing important information for use in medication development, chemical compound analysis, and nanotechnology. By developing new mathematical formulations and increasing the prediction capacity of topological indicators in nano-material science, this study advances chemical graph theory.
Topological Invariants on Line Graphs of Silicate and Silicate Sheets
(Library Information Services, CUI Lahore, 2022) Muhammad Abubaker; SP21-RMT-026; Prof. Dr. Muhammad Hussain
silicate sheets. A topological index is a numerical descriptor of the molecular structure derived from the corresponding molecular graph. These topological indices are used for the physical and chemical properties of structures. First of all, we will sketch the line graph of silicate and silicate sheets and construct the edge partition table for vertex degree based. Then we will apply different degree based topological indices on calculated data. Vertex degree base topological indices which we are going to use are such as General Randic index, harmonic index, geometric arithmetic index, atom-bond-connectivity index, symmetric division deg index, inverse-sum indeg index, forgotten index, Gourava indices, first, second and third Zagreb indices, augmented Zagreb index and hyper Zagreb index.