eng Shahid Rajaee Teacher Training University Journal of Mathematical Nanoscience 2538-2314 2538-2314 2016-06-01 6 1 1 16 10.22061/jmns.2016.498 498 Some topological indices of fluorographene P. Padmapriya 1 Veena Mathad veena_mathad@rediffmail.com 2 Department of Studies in Mathematics University of Mysore, Manasagangotri Mysuru - 570 006, INDIA Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru570 006, INDIA ABC index, ABC4 index, Randic connectivity index, Sum connectivity index, GA index, GA5 index, harmonic index, second zagreb index and AZI of Fluorographene are computed. http://jmathnano.sru.ac.ir/article_498_5df4decb8565760f253fa3dfbf0503dc.pdf vertex degree neighborhood vertex eng Shahid Rajaee Teacher Training University Journal of Mathematical Nanoscience 2538-2314 2538-2314 2016-06-01 6 1 17 26 10.22061/jmns.2016.499 499 On the energy of fullerene graphs Mahin Songhori 1 Modjtaba Ghorbani mghorbani@srttu.edu 2 Srtt University Srtt University The concept of energy of graph is defined as the sum of the absolute values of the eigenvalues of a graph. Let λ1, λ2, . . . , λn be eigenvalues of graph G, then the energy of G is defined as E (G) =∑nn=1|λه|. The aim of this paper is to compute the eigenvalues of two fullerene graphs C60 and C80. http://jmathnano.sru.ac.ir/article_499_faa8e7b92578011860e34d3297b957c0.pdf eigenvalue fullerene graph energy eng Shahid Rajaee Teacher Training University Journal of Mathematical Nanoscience 2538-2314 2538-2314 2016-06-01 6 1 27 40 10.22061/jmns.2016.510 510 New version of degree-based topological indices of certain nanotube Vijayalaxmi Shigehalli shigehallivs@yahoo.co.in 1 Rachanna Kanabur 2 Department of Mathematics, Rani Channamma University, Belagavi - 591156, Karnataka, India Department of Mathematics, Rani Channamma University, Belagavi - 591156, Karnataka, India In this paper, computation of the Arithmetic-Geometric index (AG1 index), SK index, SK1 index and SK2 index of H-Naphtalenic nanotube and TUC4[m,n] nanotube. We also compute SK3 index, AG2 index for H-Naphtalenic nanotube and TUC4[m,n] nanotube. http://jmathnano.sru.ac.ir/article_510_b57b3788f3a5c827266b7158bf794149.pdf Arithmetic-Geometric index (AG1 index) SK index SK1 index SK2 index SK3 index AG2 index H-naphtalenic nanotube TUC4[m n] nanotube eng Shahid Rajaee Teacher Training University Journal of Mathematical Nanoscience 2538-2314 2538-2314 2016-06-01 6 1 41 46 10.22061/jmns.2016.515 515 A study on Landau levels in thin films Fatemeh Ahmadi 1 Mehdi Saadat 2 Zainab Bahrampori 3 Department of Physics, Shahid Rajaee Teacher Training University Department of Physics, Shahid Rajaee Teacher Training University Department of Physics, Shahid Rajaee Teacher Training University In 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. http://jmathnano.sru.ac.ir/article_515_24e353151333ae49fb40c018acc636da.pdf thin film landau gauge energy levels wavefunctions eng Shahid Rajaee Teacher Training University Journal of Mathematical Nanoscience 2538-2314 2538-2314 2016-06-01 6 1 47 55 10.22061/jmns.2016.525 525 Computing Degree-Based Topological Indices of Polyhex Nanotubes Vijayalaxmi Shigehalli shigehallivs@yahoo.co.in 1 Rachanna Kanabur rachukanabur@gmail.com 2 Rani Channamma University, Belagavi-591156, Karnataka, India. RANI CHANNAMMA University, BELAGAVI-591156 Recently, Shigehalli and Kanabur  have put forward for new degree based topological indices, namely Arithmetic-Geometric index (AG1 index), SK index, SK1 index and SK2 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. http://jmathnano.sru.ac.ir/article_525_176ac125da5ece92fd8e1dfd11484f60.pdf Chemical graph Degree-Based Topological Indices Polyhex Nanotube eng Shahid Rajaee Teacher Training University Journal of Mathematical Nanoscience 2538-2314 2538-2314 2016-06-01 6 1 57 65 10.22061/jmns.2016.524 524 Vertex weighted Laplacian graph energy and other topological indices Reza Sharafdini sharafdini@gmail.com 1 Habibeh Panahbar panahb@gmail.com 2 Persian Gulf University Department of Mathematics, Faculty of Science, Persian Gulf University, Bushehr 7516913817, I. R. Iran Let \$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. http://jmathnano.sru.ac.ir/article_524_a66841304a42378bd6981419a07ab559.pdf energy of graph Laplacian energy Vertex weight Topological index toroidal fullerenes