Topological indices(TIs)have been practiced for distinct wide-ranging physicochemical applications,especially used to characterize and model the chemical structures of various molecular compounds such as dendrimers,na...Topological indices(TIs)have been practiced for distinct wide-ranging physicochemical applications,especially used to characterize and model the chemical structures of various molecular compounds such as dendrimers,nanotubes and neural networks with respect to their certain properties such as solubility,chemical stability and low cytotoxicity.Dendrimers are prolonged artificially synthesized or amalgamated natural macromolecules with a sequential layer of branches enclosing a central core.A present-day trend in mathematical and computational chemistry is the characterization of molecular structure by applying topological approaches,including numerical graph invariants.Among topological descriptors,Zagreb connection indices(ZCIs)have much importance.This manuscript involves the establishment of general results to calculate ZCIs,namely first ZCI(FZCI),second ZCI(SZCI),third ZCI(TZCI),modified FZCI,modified SZCI and modified TZCI of two special types of dendrimers nanostars,namely,poly propylene imine octamin(PPIO)dendrimer and poly(propyl)ether imine(PPEtIm)dendrimer.Furthermore,we provide the numerical and graphical comparative analysis of our calculated results for both types of dendrimers with each other.展开更多
The problem of investigating the minimum set of landmarks consisting of auto-machines(Robots)in a connected network is studied with the concept of location number ormetric dimension of this network.In this paper,we st...The problem of investigating the minimum set of landmarks consisting of auto-machines(Robots)in a connected network is studied with the concept of location number ormetric dimension of this network.In this paper,we study the latest type of metric dimension called as local fractional metric dimension(LFMD)and find its upper bounds for generalized Petersen networks GP(n,3),where n≥7.For n≥9.The limiting values of LFMD for GP(n,3)are also obtained as 1(bounded)if n approaches to infinity.展开更多
Dendrimers are man-made polymeric macromolecules created from branching chains known as monomers. Topological indices (TIs) are molecular descriptors that define the structure and aid in establishing relationships wit...Dendrimers are man-made polymeric macromolecules created from branching chains known as monomers. Topological indices (TIs) are molecular descriptors that define the structure and aid in establishing relationships with various physicochemical properties such as volatility, density, melting point, and more. TIs are categorized according to their distance, spectrum, and degree. Within these TIs, topological descriptors based on connection numbers (CN) hold significant importance. In this article, we calculate the overall outcomes of Zagreb connection indices, including the inverse sum connection index (ISCI), geometric arithmetic connection index (GACI), harmonic connection index (HCI), atom bond connectivity connection index (ABCCI), hyper Zagreb connection index (HZCI), and symmetric division connection index (SDCI) for the polypropyleneimine anoctamin (PPIO) dendrimer and Poly(Propyl) Ether Imine (PPEI) dendrimers. PPIO dendrimers and PPEI dendrimers are a new class of versatile nanostructured materials capable of exhibiting extraordinary physicochemical properties, which are closely related to their intricate tree-like architecture. PPIO dendrimers (synthesized using polypropylene imine) are relatively biocompatible and show promise as drug carriers, mainly because their core is hydrophobic with a hydrophilic surface. The PPEI dendrimers are highly soluble in alcohols and water and offer the ability to introduce a versatile range of functionalities. Their controlled structure, stability and tunable surface functionalities make these dendrimers attract much attention in several fields like biomedical applications, catalysis and nanotechnology. Additionally, a comparative analysis is performed to validate the excellence of our generated graphical and numerical outcomes.展开更多
Topological indices(TIs)have been found to be extensively useful in describ-ing and simulating the chemical structure of diverse molecular compounds,including dendrimers,nanotubes,and neural networks.Dendrimers repres...Topological indices(TIs)have been found to be extensively useful in describ-ing and simulating the chemical structure of diverse molecular compounds,including dendrimers,nanotubes,and neural networks.Dendrimers represent a distinct class of well-defined,highly branched macromolecules characterized by their symmetrical,tree-like architecture.This review provides a compre-hensive overview of dendrimer synthesis,structure,properties,and diverse applications in nanoscience.Currently,the field of chemistry is actively ex-ploring a mathematical approach that involves using topological techniques and numerical graph invariants to characterize molecular structures.Out of all the established descriptors,connection-based Zagreb indices are generally regarded as more efficient than the traditional indices.This manuscript pre-sents the overarching outcome for calculating the Zagreb connection indices,specifically,harmonic connection index(HCI),augmented connection index(ACI),symmetric division connection index(SDCI),geometric arithmetic connection index(GACI),hyper Zagreb connection index(HZCI),inverse sum connection index(ISCI),and atom bond connectivity connection index(ABCCI).Furthermore,we compare the numerical and graphical values with each other to assess their relative superiority.展开更多
文摘Topological indices(TIs)have been practiced for distinct wide-ranging physicochemical applications,especially used to characterize and model the chemical structures of various molecular compounds such as dendrimers,nanotubes and neural networks with respect to their certain properties such as solubility,chemical stability and low cytotoxicity.Dendrimers are prolonged artificially synthesized or amalgamated natural macromolecules with a sequential layer of branches enclosing a central core.A present-day trend in mathematical and computational chemistry is the characterization of molecular structure by applying topological approaches,including numerical graph invariants.Among topological descriptors,Zagreb connection indices(ZCIs)have much importance.This manuscript involves the establishment of general results to calculate ZCIs,namely first ZCI(FZCI),second ZCI(SZCI),third ZCI(TZCI),modified FZCI,modified SZCI and modified TZCI of two special types of dendrimers nanostars,namely,poly propylene imine octamin(PPIO)dendrimer and poly(propyl)ether imine(PPEtIm)dendrimer.Furthermore,we provide the numerical and graphical comparative analysis of our calculated results for both types of dendrimers with each other.
基金funded by the Deanship of Scientific Research at Jouf University under Grant No.DSR-2021-03-0301supported by the Higher Education Commission of Pakistan through the National Research Program for Universities Grant No.20-16188/NRPU/R&D/HEC/20212021.
文摘The problem of investigating the minimum set of landmarks consisting of auto-machines(Robots)in a connected network is studied with the concept of location number ormetric dimension of this network.In this paper,we study the latest type of metric dimension called as local fractional metric dimension(LFMD)and find its upper bounds for generalized Petersen networks GP(n,3),where n≥7.For n≥9.The limiting values of LFMD for GP(n,3)are also obtained as 1(bounded)if n approaches to infinity.
文摘Dendrimers are man-made polymeric macromolecules created from branching chains known as monomers. Topological indices (TIs) are molecular descriptors that define the structure and aid in establishing relationships with various physicochemical properties such as volatility, density, melting point, and more. TIs are categorized according to their distance, spectrum, and degree. Within these TIs, topological descriptors based on connection numbers (CN) hold significant importance. In this article, we calculate the overall outcomes of Zagreb connection indices, including the inverse sum connection index (ISCI), geometric arithmetic connection index (GACI), harmonic connection index (HCI), atom bond connectivity connection index (ABCCI), hyper Zagreb connection index (HZCI), and symmetric division connection index (SDCI) for the polypropyleneimine anoctamin (PPIO) dendrimer and Poly(Propyl) Ether Imine (PPEI) dendrimers. PPIO dendrimers and PPEI dendrimers are a new class of versatile nanostructured materials capable of exhibiting extraordinary physicochemical properties, which are closely related to their intricate tree-like architecture. PPIO dendrimers (synthesized using polypropylene imine) are relatively biocompatible and show promise as drug carriers, mainly because their core is hydrophobic with a hydrophilic surface. The PPEI dendrimers are highly soluble in alcohols and water and offer the ability to introduce a versatile range of functionalities. Their controlled structure, stability and tunable surface functionalities make these dendrimers attract much attention in several fields like biomedical applications, catalysis and nanotechnology. Additionally, a comparative analysis is performed to validate the excellence of our generated graphical and numerical outcomes.
文摘Topological indices(TIs)have been found to be extensively useful in describ-ing and simulating the chemical structure of diverse molecular compounds,including dendrimers,nanotubes,and neural networks.Dendrimers represent a distinct class of well-defined,highly branched macromolecules characterized by their symmetrical,tree-like architecture.This review provides a compre-hensive overview of dendrimer synthesis,structure,properties,and diverse applications in nanoscience.Currently,the field of chemistry is actively ex-ploring a mathematical approach that involves using topological techniques and numerical graph invariants to characterize molecular structures.Out of all the established descriptors,connection-based Zagreb indices are generally regarded as more efficient than the traditional indices.This manuscript pre-sents the overarching outcome for calculating the Zagreb connection indices,specifically,harmonic connection index(HCI),augmented connection index(ACI),symmetric division connection index(SDCI),geometric arithmetic connection index(GACI),hyper Zagreb connection index(HZCI),inverse sum connection index(ISCI),and atom bond connectivity connection index(ABCCI).Furthermore,we compare the numerical and graphical values with each other to assess their relative superiority.
