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EXTREMAL CHEMICAL TREES WITH RESPECT TO HYPER-ZAGREB INDEX
Ali Ghalavand,Ali Reza Ashrafi,Reza Sharafdini,Ottorino Ori 한국수학교육학회 2019 純粹 및 應用數學 Vol.26 No.3
Suppose G is a molecular graph with edge set E(G). The Hyper-Zagreb index of G is defined as $ HM(G)=sum_{uv\in E(G)}[deg_{G}(u) + deg_{G}(v)]^2$, where $deg_G(u)$ is the degree of a vertex u in G. In this paper, we characterize the chemical trees of order $n=> 12$ with the first twenty smallest Hyper-Zagreb index are characterized.
Majdedin Ghalavand,Mojtaba Saadati,Jafar Salimian,Ebrahim Abbasi,Ghader Hosseinzadeh,Hadi Esmaeili Gouvarchin Ghaleh,Ali Ahmadi 대한백신학회 2021 Clinical and Experimental Vaccine Research Vol.10 No.1
Purpose: Chitosan is a natural polymer that has excellent properties include biocompatibility, biodegradability, no cytotoxicity, high charge density, low cost, mucoadhesive, permeation enhancing (ability to cross tight junction), and immunomodulating ability that makes the spectrum of its applicability much broader. This study was conducted to investigate the stabilizing, preservative and immunogenicity properties of N-trimethyl chitosan nanospheres (N-TMCNS). Materials and Methods: The tetanus toxoid (TT) was encapsulated into N-TMCNS and then characterized by scanning electron microscope, atomic force microscope, and dynamic light scattering. For stabilizer assay of N-TMCNS after storage of TT-N-TMCNS at different temperatures for 3 weeks, they were used for immunization of mice and different temperatures groups’ anti-TT-N-TMCNS production compared with other groups. Finally, the immunized mice were challenged with tetanus toxin. The preservation activity of TT-N-TMCNS against Escherichia coli was compared with thimerosal formulated TT. Results: Our results revealed that heat-treated TT-N-TMCNS could induce higher titer of neutralizing immunoglobulin G in compared to TT vaccine and was able to protect the mice better than TT vaccine in challenge test. Furthermore, N-TMCNS as a preservative inhibited the growth of E. coli more effective than thimerosal. Conclusion: Overall, the obtained results indicated that the N-TMCNS is one of the best stabilizer and preservative agent that can be used in the formulation of TT vaccine.
On Diameter, Cyclomatic Number and Inverse Degree of Chemical Graphs
Reza Sharafdini,Ali Ghalavand,Ali Reza Ashrafi 경북대학교 자연과학대학 수학과 2020 Kyungpook mathematical journal Vol.60 No.3
Let G be a chemical graph with vertex set {v1, v1, . . . , vn} and degree sequence d(G) = (degG(v1), degG(v2), . . . , degG(vn)). The inverse degree, R(G) of G is defined as R(G) = Pni=11degG(vi). The cyclomatic number of G is defined as γ = m − n + k, where m, n and k are the number of edges, vertices and components of G, respectively. In this paper, some upper bounds on the diameter of a chemical graph in terms of its inverse degree are given. We also obtain an ordering of connected chemical graphs with respect to the inverse degree.