University of KashanIranian Journal of Mathematical Chemistry2228-648912320210901On the Trees with Given Matching Number and the Modified First Zagreb Connection Index12713811151510.22052/ijmc.2021.242169.1554ENSadiaNoureenDepartment of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, B-Block, Faisal Town, Lahore, PakistanDepartment of Mathematics, Faculty of Science, University of Gujrat, Gujrat, PakistanAkhlaqAhmad BhattiDepartment of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, B-Block, Faisal Town, Lahore, PakistanJournal Article20210329The modified first Zagreb connection index ZC<sup>∗</sup><sub>1</sub> for a graph G is defined as ZC<sup>∗</sup><sub>1</sub> (G) = \sum v∈V (G) d<sub>v</sub>τ<sub>v</sub> , where d<sub>v</sub> is the degree of the vertex v and τ<sub>v</sub> denotes the connection number of v (that is, the number of vertices at the distance 2 from the vertex v). Let T<sub>n,α</sub> be the class of trees with order n and matching number α such that n > 2α−1. In this paper, we obtain the lower bounds on the modified first Zagreb connection index of trees belonging to the class Tn,α, for 2α − 1 < n < 3α + 2.https://ijmc.kashanu.ac.ir/article_111515_484b409936d065a89799b3a7e36adc56.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648912320210901Resolvent Energy of Digraphs13915911162510.22052/ijmc.2021.242877.1562ENEffatGolpar-RabokyDepartment of Mathematics, Qom, IranAzamBabaiDepartment of Mathematics, Qom, IranJournal Article20210603In this paper, we present two approaches to compute the resolvent energy of a digraph . The first method computes the energy by ER(G)=\sum_{i=1})^n\frac{1}{n-Re(z_i)}, where Re(z<sub>_</sub>i )denotes the real part of the eigenvalue z_i of G. In the second method we define ER(G)=\sum_{i=1}^n\frac{1}{n-σ_i}, where σ_i is the ith singular value of G. We prove some properties of resolvent energy for some special digraphs and determine the resolvent energy of unicyclic and bicyclic digraphs and present lower bound for resolvent energy of directed cycles.https://ijmc.kashanu.ac.ir/article_111625_6834418b07b921bb7e2d4640c01b3370.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648912320210901Computing the Hosoya and the Merrifield-Simmons Indices of Two Special Benzenoid Systems16117411162610.22052/ijmc.2021.243008.1580ENMert SinanOzFaculty of Engineering and Natural Sciences, Department of Mathematics, Bursa Technical University, 16320 Bursa, TurkeyIsmail NaciCangulFaculty of Arts and Science, Department of Mathematics, Bursa Uludag University, 16059 Bursa, TurkeyJournal Article20210811Gutman et al. gave some relations for computing the Hosoya indices of two special benzenoid systems R_n and P_n. In this paper, we compute the Hosoya index and Merrifield-Simmons index of R_n and P_n by means of introducing four vectors for each benzenoid system and index. As a result, we compute the Hosoya index and the Merrifield-Simmons index of R_n and P_n by means of a product of a certain matrix of degree n and a certain vector.https://ijmc.kashanu.ac.ir/article_111626_d24057b37779e563f00bfba51b20476f.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648912320210901Controlled Synthesis Of One Dimensional Zinc Oxide Nanostructures in terms of Modelling17518511157010.22052/ijmc.2021.243007.1579ENMushtaqueHussainNED University Of Engineering &amp; Technology, Karachi, PakistanSyed HashmatHikmatNED University ,University RoadAzamKhanNED UniversityJournal Article20210810In the present work, a Mathematical model is proposed for the control on the concentration of hydroxyl ion in the precursor solution to preserve low super saturation level, because in order to obtain the desired and high quality one dimensional Zinc oxide nanostructures it is important to control the super saturation of the reactants. It was observed that elevated super saturation amount support nucleation and moderate super saturation amount support crystal growth during the synthesis of one dimensional Zinc oxide nanostructures. The kinematic reactions in the precursor solution were observed with the help of Lengyel-Epistein theory. Experimentally, the synthesis of ZnO nanostructures was also performed through Aqueous chemical growth method.https://ijmc.kashanu.ac.ir/article_111570_814550fd8508975b2740c751d9dffd43.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648912320210901Exponential Growth of Graph Resolvent18719511163110.22052/ijmc.2022.242190.1556ENAli A.ShukurComputer Technical Engineering Department, College of Technical Engineering, The Islamic University, Najaf, Iraq
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Faculty of Mechanics and Math, Belarusian State University, BelarusJournal Article20210408The spectrum of arbitrary graph of finite order the exponential growth of the resolvent of graph G is one of the most investigated object during the last 50 years. In particular, the resolvent matrix is a matrix with property that all of its eigenvalues are outside the spectra of G. In this paper, we study the exponential growth of the resolvent of graph G. The exponential growth of resolvent energy of graph G was investigated.https://ijmc.kashanu.ac.ir/article_111631_c21beb412fef5d68057763c6aff1bf50.pdf