Sarfraz Ahmad

Sarfraz Ahmad
COMSATS University Islamabad | CUI · Department of Mathematics

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56
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631
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Introduction

Publications

Publications (56)
Article
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In this article, we present the concept of extended Seidel energy by employing a generalized extended matrix to study various molecular properties, including the Kovats retention index, boiling point, enthalpy of formation, entropy, acentric factor, and octanol-water partition coefficient. Our research broadens the scope of energy matrices in graph...
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For a poset P = C a × C b , a subset A ⊆ P is called a chain blocker for P if A is inclusion wise minimal with the property that every maximal chain in P contains at least one element of A, where C i is the chain 1 < · · · < i. In this article, we define shelter of the poset P to give complete description of all chain blockers of C 5 × C b for b ≥...
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A polymer is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. The bulky and normal polymers are graphs of aromatic organic compounds. The main idea of this article is to elaborate the expected results of Zagreb connection, sombor and reduced sombor indices in bulky and normal pol...
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Mathematical chemistry plays a vital role in investigating the metal-insulator transition Superlattice (GST-SL) of strongly correlated 3D electrons due to quantum confinement. The development of epitaxial GST-SL thin films with the design of heterogenous openings is of extraordinary interest due to their applications. The thin-film declaration and...
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Glycogen is a polysaccharide that has a large number of highly branched polymers. It has a structure that is nearly identical to that of amylopectin. It can be found in practically all animal cells and some plant cells. Glycogen is a natural polysaccharide polymer with features that make it a good antiparticle carrier for cancer therapeutics. It is...
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Let G be the graph and the energy of graph G is depend on the summation of its absolute eigenvalues. We study the Randic, Seidel,and Laplacian energies of graph G where G is the non-extended p-sum of the graphs. We show that the energy of graph is depend on the base elements and how this result is used to generalize the concept of energies. We are...
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Dendrimer designs include three distinct parts: a focal point, an interior construction with repetitive branches, and an exterior design with practical gatherings. Dendrimers are a new class of polymeric materials. They are fabricated three dimensional, mano-disperse structure having tree like branches. Dendrimers are also called arborols and casca...
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The silicon material has provoked and stimulated significant research concern to a considerable extent taking into account its marvelous mechanical, optical, and electronic properties. Naturally, silicons are semiconductors and are utilized in the formation of various materials. For example, it is used in assembling the electronic based gadgets. In...
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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 d...
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In chemical graph theory, benzenoid systems are interrogated as they exhibit the chemical compounds known as benzenoid hydrocarbons. Benzenoid schemes are circumscribed as planar connected finite graphs having no cut vertices wherein the entire internal sections are collaboratively congruent regular hexagon. The past couple of decennium has acknowl...
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Biological proceedings are well characterized by solid illustrations for communication networks. The framework of biological networks has to be considered together with the expansion of infectious diseases like coronavirus. Also, the graph entropies have established themselves as the information theoretic measure to evaluate the architectural infor...
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The eccentricity-based entropy inspired by Shannon's entropy approach is the information-theoretic quantity to figure out the structural information of complex networks. The investigation for advance biomedical utilization of dendrimers has improved the synthesis of radical based molecules. Categorically, attaining radical dendrimers has initiated...
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In recent years, the study of topological indices associated to different molecular tubes and structures gained a lot of attention of the researchers—working in Chemistry and Mathematics. These descriptors play an important role in describing different properties associated to the objects of study. Moreover, Shannon’s entropy concept—a slightly dif...
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Two-dimensional materials have fascinated extensive attention due to their novel optical and mechanical properties for prospective applications. In (QSPR/QSAR) studies, the biological activity of underlying structure is associated with physical properties of structure by using topological indices. A huge spectrum of topological indices is available...
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Lot of achievements have been done to comprehend the latest phenomena of our life by discussing the interrelationship of two boughs, graph theory and algebra, of mathematics. In the modern time, it seems to be of great importance to study about eminent, extensive and certifiable applications through well known tools of graph theory. Combinatorial c...
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The graph entropy is an important quantity of information theory. It measures the structural information of chemical graphs and complex networks. The graph entropy measures have specific chemical applications in discrete mathematics, biology and chemistry. The main contribution of this paper is to study properties of graph entropies and then goes o...
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The entropy-based procedures from the configuration of chemical graphs and multifaceted networks, several graph properties have been utilized. For computing, the organizational evidence of organic graphs and multifaceted networks, the graph entropies have converted the information-theoretic magnitudes. The graph entropy portion has attracted the re...
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Background: Topological indices have numerous implementations in chemistry, biology and a lot of other areas. It is a real number associated with a graph, which provides information about its physical and chemical properties and their correlations. For a connected graph H, the degree distance DD index is defined as DD(H) = Σ{h1,h2}⊆V(H) [degH(h1)+...
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A zero-sum flow is an assignment of nonzero integers to the edges such that the sum of the values of all edges incident with each vertex is zero, and we call it a zero-sum k-flow if the absolute values of edges are less than k. We define the zero-sum flow number of G as the least integer k for which G admitting a zero sum k-flow.? ?In this paper we...
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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 chemic...
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Let G be a molecular graph with n vertices, m edges and L(G) be the line graph of G. Both G and L(G) can be represented by their adjacency matrices A and E, respectively. The eigenvalues of G and L(G) are denoted by, �1 ⩾ �2 ⩾ ::: ⩾ �n and 1 ⩾ 2 ⩾ ::: ⩾ n, respectively. The Estrada index A and L(G) are de�ned as EE(G) = Σn i=1 e�i and EE(L) = Σn...
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Let G be a molecular graph with n vertices, m edges and G(L) be a line graph. Both G and L can be represented by their adjacency matrices A and E, respectively. The eigenvalues of G and L are denoted by, λ1⩾λ2⩾…⩾λn and γ1⩾γ2⩾…⩾γn, respectively. The Estrada index A and L are defined as EE(G)=∑i=1neλi and EE(L)=∑i=1neγi. In this article, we present s...
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Topological indices as a molecular descriptors are important tools in (QSAR)/(QSPR) studies. The graph entropies with topological indices inspired by Shannon’s entropy concept become the information-theoretic quantities for measuring the structural information of chemical graphs and complex networks. The graph entropy measures are playing an import...
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The nanostar dendrimers are a piece of another gathering of macromolecules that seem, by all accounts, to be photon pipes simply like counterfeit reception apparatuses. In addition, nanostar dendrimers are one of the fundamental stuffs of nanobiotechnology. The smart polymers are large-scale particles that show an emotional physioconcoction change...
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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 num...
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The latest developments in algebra and graph theory allow us to ask a natural question, what is the application in real world of this graph associated with some mathematical system? Groups can be used to construct new non-associative algebraic structures, loops. Graph theory plays an important role in various fields through edge labeling. In this p...
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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 compu...
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The Chemical graph theory is extensively used in finding the atomic supplementary properties of different chemical stuructures. Many results of graph theory are commonly used in molecular structures and in general in Chemisty. In a molcular graph vertices are atoms while chemical bonds are given by edges. This article is about computing the exact v...
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A zero-sum flow is an assignment of nonzero integers to the edges such that the sum of the values of all edges incident with each vertex is zero, and we call it a zero-sum k-flow if the absolute values of edges are less than k. We recall the zero-sum flow number of G as the least integer k for which G admitting a zero sum k-flow. In this paper we g...
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Let G=V,E be a simple connected graph, w∈V be a vertex, and e=uv∈E be an edge. The distance between the vertex w and edge e is given by de,w=mindw,u,dw,v , A vertex w distinguishes two edges e1 , e2∈E if dw,e1≠dw,e2 . A set S is said to be resolving if every pair of edges of G is distinguished by some vertices of S . A resolving set with minimum ca...
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Owing to their distinguished properties, titanium difluoride (TiF 2) and the crystallographic structure of Cu 2 O have attracted a great deal of attention in the field of quantitative structure-property relationships (QSPRs) in recent years. A topological index of a diagram (G) is a numerical quantity identified with G which portrays the sub-atomic...
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A graph invariant is a numerical value that depicts the structural properties of an entire graph. The Wiener index is the oldest distance based graph invariant which is defined as the sum of distances between all unordered pair of vertices of the graph G. In this paper we use the method of edge cut to compute the Wiener index and Wiener polarity in...
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A simple graph G(V, E) admits a H-covering, if every edge in E(G) belongs to a subgraph of G isomorphic to H. The graph G is said to be H-magic, if there exists a bijection ψ: V(G) ∪ E(G) → {1, 2, 3, … ,|V(G)|+|E(G)|} such that for every subgraph H¢ of G isomorphic to is constant. Moreover G is said to be H-super magic, if ψ (V(G)) = {1, 2, 3, … ,|...
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A variety of dendrimers exist, and each has biological properties such as polyvalency, selfassembling, electrostatic interactions, chemical stability, low cytotoxicity, and solubility. These varied characteristics make dendrimers a good choice in the medical field and pharmaceuticals. A topological index is actually designed by transforming a molec...
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The counting polynomials are useful in topological description of benzenoid structures. It also helps to describe its topological indices by virtue of quasi-orthogonal cuts of the edge strips in the polycyclic graphs. In this article we give a complete description of the Omega and the Sadhana polynomial of the nanotube C4C6C8 and provide its mathem...
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The lth partial barycentric subdivision is defined for a (d-1)-dimensional simplicial complex \Delta and studied along with its combinatorial, geometric and algebraic aspects. We analyze the behavior of the f- and h-vector under the lth partial barycentric subdivision extending previous work of Brenti and Welker on the standard barycentric subdivis...
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In QSAR/QSPR study, the topological indices are being utilized to predict the bioactivity of certainchemical compounds. These indices are very important in mathematical chemistry. In this article, wegive a complete description of the certain Zagreb indices of the TUC5C8nanotubes. We also givean explicit formulae of geometric-arithmetic index, the R...
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In theoretical and computational chemistry, a molecular descriptor 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. Valency based topological descriptors like atom-bond connectivity index and...
Article
Full-text available
In QSAR/QSPR study, the topological indices are being utilized to predict the bioactivity of certain chemical compounds. These indices are very important in mathematical chemistry. In this article, we give a complete description of the certain Zagreb indices of the TUC5C8 nanotubes. We also give an explicit formulae of geometric-arithmetic index, t...
Article
Full-text available
The counting polynomials are useful in topological description of benzenoid structures. The quasi-orthogonal cut strips could account for the helicity of nanotubes and nanotori. It also helps to describe its topological indices by virtue of quasi-orthogonal cuts of the edge strips in the polycyclic graphs. In this article, we give a complete descri...
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In QSAR/QSPR studies, topological indices are utilized to predict the bioactivity of chemical compounds. In this paper, the closed forms of different Zagreb indices and atom–bond connectivity indices of regular dendrimers G [ n ] and H [ n ] in terms of a given parameter n are determined by using the auto­morphism group action. It was reported that...
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Let J ⊂ I be two monomial ideals such that I/J is Cohen Macaulay. By associating a finite posets PI/Jg$P_{I/J}^g$ to I/J, we show that if I/J is a Stanley ideal then I/J˜$\widetilde{I/J}$ is also a Stanley ideal, where I/J˜$\widetilde{I/J}$ is the polarization of I/J. We also give relations between sdepth and fdepth of I/J and I/J˜$\widetilde{I...
Article
Let K be a field and S = K[x1,.,xn] be the polynomial ring in n variables. Let I ⊂ S be a monomial ideal such that S/I is Cohen-Macaulay. By associating a finite poset PS/Ig to S/I, we show that if S/I is a Stanley ideal then T/Ï is also a Stanley ideal, where T = K[x11,.,x1a1,.,xn1,.,xnan] and I is the polarization of I. © 2015 Academy of Mathemat...
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For a simplicial complex Δ we study the behavior of its f- and h-triangle under the action of barycentric subdivision. In particular we describe the f- and h-triangle of its barycentric subdivision sd(Δ). The same has been done for f- and h-vector of sd(Δ) by F. Brenti, V. Welker (2008). As a consequence we show that if the entries of the h-triangl...
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In this paper,we introduce the monomial ideals I(H) associated to a special class of non uniform hypergraphs H(X; E; d) namely uniformly increasing hypergraphs. These ideals are named as inclusion ideals. In this paper, we discuss some algebraic properties of these inclusion ideals. In particular, we give an upper bound of the Castlenouvo-Mumford r...
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In this paper, we introduce the concept of f-ideals and discuss its algebraic properties. In particular, we give the characterization of all the f-ideals of degree 2.
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We define nice partitions of the multicomplex associated with a Stanley ideal. As the main result we show that if the monomial ideal I is a CM Stanley ideal, then I p is a Stanley ideal as well, where I p is the polarization of I.
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We show that the regularity of monomial ideals of K[x1,…, xn] (K being a field), whose associated prime ideals are totally ordered by inclusion is upper bounded by a linear function in n.
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Let $I$ be a monomial ideal of the polynomial ring $S=K[x_1,...,x_4]$ over a field $K$. Then $S/I$ is sequentially Cohen-Macaulay if and only if $S/I$ is pretty clean. In particular, if $S/I$ is sequentially Cohen-Macaulay then $I$ is a Stanley ideal.
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We show that the regularity of monomial ideals whose associated prime ideals are totally ordered by inclusion is linearly bounded.

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