Shahid Rajaee Teacher Training UniversityJournal of Mathematical Nanoscience2538-23146120160601Some topological indices of fluorographene11649810.22061/jmns.2016.498ENP.PadmapriyaDepartment of Studies in Mathematics
University of Mysore, Manasagangotri
Mysuru - 570 006, INDIAVeenaMathadDepartment of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru570
006, INDIAJournal Article20160114ABC index, ABC<sub>4</sub> index, Randic connectivity index, Sum connectivity index, GA index, GA<sub>5</sub> index, harmonic index, second zagreb index and AZI of Fluorographene are computed.https://jmathnano.sru.ac.ir/article_498_5df4decb8565760f253fa3dfbf0503dc.pdfShahid Rajaee Teacher Training UniversityJournal of Mathematical Nanoscience2538-23146120160601On the energy of fullerene graphs172649910.22061/jmns.2016.499ENMahinSonghoriSrtt UniversityModjtabaGhorbaniSrtt UniversityJournal Article20160211The concept of energy of graph is defined as the sum of the absolute values of the eigenvalues of a graph. Let λ<sub>1</sub>, λ<sub>2</sub>, . . . , λ<sub>n </sub>be eigenvalues of graph G, then the energy of G is defined as E (G) =∑<sup>n</sup><sub>n=1</sub>|λ<sub>ه</sub>|. The aim of this paper is to compute the eigenvalues of two fullerene graphs C<sub>60</sub> and C<sub>80</sub>.https://jmathnano.sru.ac.ir/article_499_faa8e7b92578011860e34d3297b957c0.pdfShahid Rajaee Teacher Training UniversityJournal of Mathematical Nanoscience2538-23146120160601New version of degree-based topological indices of certain nanotube274051010.22061/jmns.2016.510ENVijayalaxmiShigehalliDepartment of Mathematics, Rani Channamma University, Belagavi - 591156, Karnataka,
IndiaRachannaKanaburDepartment of Mathematics, Rani Channamma University,
Belagavi - 591156, Karnataka, IndiaJournal Article20150802In this paper, computation of the Arithmetic-Geometric index (AG1 index), SK index, SK<sub>1</sub> index and SK<sub>2</sub> index of H-Naphtalenic nanotube and TUC<sub>4</sub>[m,n] nanotube. We also compute SK<sub>3</sub> index, AG<sub>2</sub> index for H-Naphtalenic nanotube and TUC<sub>4</sub>[m,n] nanotube.https://jmathnano.sru.ac.ir/article_510_b57b3788f3a5c827266b7158bf794149.pdfShahid Rajaee Teacher Training UniversityJournal of Mathematical Nanoscience2538-23146120160601A study on Landau levels in thin films414651510.22061/jmns.2016.515ENFatemehAhmadiDepartment of Physics, Shahid Rajaee Teacher Training UniversityMehdiSaadatDepartment of Physics, Shahid Rajaee Teacher Training UniversityZainabBahramporiDepartment of Physics, Shahid Rajaee Teacher Training UniversityJournal Article20150902In this paper, we study the energy levels of an electron moving in a thin film. This film is considered as a two-dimensional electron gas which is under the influence of a uniform external magnetic field B and a uniform external electric field E. Here, the magnetic field is perpendicular to the film. Also, in this paper, we have selected the Landau gauge, because this gauge is useful for working in rectangular geometries.https://jmathnano.sru.ac.ir/article_515_24e353151333ae49fb40c018acc636da.pdfShahid Rajaee Teacher Training UniversityJournal of Mathematical Nanoscience2538-23146120160601Computing Degree-Based Topological Indices of Polyhex Nanotubes475552510.22061/jmns.2016.525ENVijayalaxmiShigehalliRani Channamma University, Belagavi-591156, Karnataka, India.RachannaKanaburRANI CHANNAMMA University, BELAGAVI-5911560000000174967503Journal Article20160812Recently, Shigehalli and Kanabur [20] have put forward for new degree based topological indices, namely Arithmetic-Geometric index (AG1 index), SK index, SK<sub>1</sub> index and SK<sub>2</sub> index of a molecular graph G. In this paper, we obtain the explicit formulae of these indices for Polyhex Nanotube without the aid of a computer.https://jmathnano.sru.ac.ir/article_525_176ac125da5ece92fd8e1dfd11484f60.pdfShahid Rajaee Teacher Training UniversityJournal of Mathematical Nanoscience2538-23146120160601Vertex weighted Laplacian graph energy and other topological indices576552410.22061/jmns.2016.524ENRezaSharafdiniPersian Gulf UniversityHabibehPanahbarDepartment of Mathematics, Faculty of Science, Persian Gulf University, Bushehr 7516913817,
I. R. IranJournal Article20160803Let $G$ be a graph with a vertex weight $omega$ and the vertices $v_1,ldots,v_n$. The Laplacian matrix of $G$ with respect to $omega$ is defined as $L_omega(G)=diag(omega(v_1),cdots,omega(v_n))-A(G)$, where $A(G)$ is the adjacency matrix of $G$. Let $mu_1,cdots,mu_n$ be eigenvalues of $L_omega(G)$. Then the Laplacian energy of $G$ with respect to $omega$ defined as $LE_omega (G)=sum_{i=1}^nbig|mu_i - overline{omega}big|$, where $overline{omega}$ is the average of $omega$, i.e., $overline{omega}=dfrac{sum_{i=1}^{n}omega(v_i)}{n}$. In this paper we consider several natural vertex weights of $G$ and obtain some inequalities between the ordinary and Laplacian energies of $G$ with corresponding vertex weights. Finally, we apply our results to the molecular graph of toroidal fullerenes (or achiral polyhex nanotorus).\[5mm] noindenttextbf{Key words:} Energy of graph, Laplacian energy, Vertex weight, Topological index, toroidal fullerenes.https://jmathnano.sru.ac.ir/article_524_a66841304a42378bd6981419a07ab559.pdf