Shahid Rajaee Teacher Training University Journal of Mathematical Nanoscience 2538-2314 7 1 2017 06 01 How to struggle with the beauty and symmetry of soccer ball fullerene–personal history 1 14 EN Haruo Hosoya Ochanomizu University (Emeritus), Bunkyo-ku, Tokyo 112-8610, Japan On this occasion I thought that it is meaningful to trace back and document my personal history involved in this beautiful soccer ball shape and molecule C60 not only for myself but also for the next generation to follow. Therefore, the topics may be moving to and fro in the 4-dimensional world. If the readers find any inaccurate description, please, remind its correctionsor additions to me privately or to the public freely. http://jmathnano.sru.ac.ir/article_704.html http://jmathnano.sru.ac.ir/article_704_216b3ce453f595b56c4c00cfb540b5b6.pdf
Shahid Rajaee Teacher Training University Journal of Mathematical Nanoscience 2538-2314 7 1 2017 06 01 On the edge energy of some specific graphs 15 21 EN Saeid Alikhani Department of Mathematics, Yazd University, 89195-741, Yazd, Iran alikhani206@gmail.com Fatemeh Mohebbi Department of Mathematics, Yazd University, 89195-741, Yazd, Iran 10.22061/jmns.2017.546 Let G = (V,E) be a simple graph. The energy of G is the sum of absolute values of the eigenvalues of its adjacency matrix A(G). In this paper we consider the edge energy of G (or energy of line of G) which is defined as the absolute values of eigenvalues of edge adjacency matrix of G. We study the edge energy of specific graphs. energy,edge energy,edge adjacency matrix,Line graph http://jmathnano.sru.ac.ir/article_546.html http://jmathnano.sru.ac.ir/article_546_f9c71ca1b8d4e4d48401276b55fec411.pdf
Shahid Rajaee Teacher Training University Journal of Mathematical Nanoscience 2538-2314 7 1 2017 06 01 The second eccentric Zagreb index of the \$N^{TH}\$ growth of nanostar dendrimer \$D_{3}[N]\$ 23 28 EN Mohammad Reza Farahani Department of Applied Mathematics, Iran University of Science and Technology (IUST), Narmak, Tehran 16844, Iran mrfarahani88@gmail.com Abdul Qudair Baig Department of Mathematics, COMSATS Institute of Information Technology, Attock Campus, Pakistan aqbaig1@gmail.com Wasim Sajjad Department of Mathematics, University of Sargodha, Mandi Bahauddin Campus, Mandi Bahauddin Pakistan wasim.sajjad89@gmail.com 10.22061/jmns.2017.670 Let G = (V,E) be an ordered pair, where V(G) is a non-empty set of vertices and E(G) is a set of edges called a graph. We denote a vertex by v, where v 2 V(G) and edge by e, where e = uv 2 E(G). We denote degree of vertex v by dv which is defined as the number of edges adjacent with vertex v.  The distance between two vertices of G is the length of a shortest path connecting these two vertices which is denoted by d(u,v) where u,v 2 V(G). The eccentricity ecc(v) of a vertex v in G is the distance between vertex v and vertex farthest from v in G. In this paper, we consider an infinite family of nanostar dendrimers and then we compute its second eccentric Zagreb index. Ghorbani and Hosseinzadeh introduced the second eccentric Zagreb index as EM2(G) = åuv2E(G) (ecc(u)  ecc(v)),that ecc(u) denotes the eccentricity of vertex u and ecc(v) denotes the eccentricity of vertex v of G. Molecular graph,Eccentricity,Zagreb topological index,nanostar dendrimer,D3[n] http://jmathnano.sru.ac.ir/article_670.html http://jmathnano.sru.ac.ir/article_670_2633e66e0388587817d173344152cf14.pdf
Shahid Rajaee Teacher Training University Journal of Mathematical Nanoscience 2538-2314 7 1 2017 06 01 Strong chromatic index of certain nanosheets 29 38 EN Vidya Ganesan School of Advanced Sciences vidyaganesan15@gmail.com Indra Rajasingh VIT University, Chennai-600127 indrarajasingh@yahoo.com 10.22061/jmns.2017.703 Strong edge-coloring of a graph is a proper edge coloring such that every edge of a path of length 3 uses three different colors. The strong chromatic index of a graph is the minimum number k such that there is a strong edge-coloring using k colors and is denoted by c′ s(G). We give efficient algorithms for strong edge-coloring of certain nanosheets using optimum number of colors. strong edge-coloring,strong chromatic index,nanosheets http://jmathnano.sru.ac.ir/article_703.html http://jmathnano.sru.ac.ir/article_703_7b6e3988c41ec6cc7c374883cff14757.pdf
Shahid Rajaee Teacher Training University Journal of Mathematical Nanoscience 2538-2314 7 1 2017 06 01 On topological properties of boron triangular sheet BTS(m,n), borophene chain B36(n) and melem chain MC(n) nanostructures 39 60 EN Haidar Ali Government College University Faisalabad Pakistan haidar3830@gmail.com Abdul Qudair Baig Department of Mathematics, COMSATS Institute of Information Technology, Attock Campus, Pakistan aqbaig1@gmail.com Muhammad Kashif Shafiq Department of Mathematics,Government College University, Faisalabad, Pakistan kashif4v@gmail.com 10.22061/jmns.2017.705 Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randic, atom-bond connectivity ´ (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study and derive analytical closed results of general Randic index ´ Rα(G) with α = 1, 1 2 ,−1,−1 2 , for boron triangular sheet BTS(m,n), borophene chain of B36(n) and melem chain MC(n). We also compute the general first Zagreb, ABC, GA, ABC4 and GA5 indices of sheet and chains for the first time and give closed formulas of these degree based indices. general Randic index,atom-bond connectivity ´ (ABC) index,geometric-arithmetic (GA) index,boron triangular,borophene,melem http://jmathnano.sru.ac.ir/article_705.html http://jmathnano.sru.ac.ir/article_705_5f1e113c297e2d34b446d432f8a75049.pdf
Shahid Rajaee Teacher Training University Journal of Mathematical Nanoscience 2538-2314 7 1 2017 06 01 On the automorphism group of cubic polyhedral graphs 61 69 EN Mahin Songhori Department of Mathematics, Shahid Rajaee Teacher Training University In the present paper, we introduce the automorphism group of cubic polyhedral graphs whose faces are triangles, quadrangles, pentagons and hexagons. polyhedral graph,automorphism group,fullerene http://jmathnano.sru.ac.ir/article_511.html http://jmathnano.sru.ac.ir/article_511_f9cb2b06dcb533937e8e7a2d15076cc6.pdf