eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2017-06-01
7
1
1
14
704
How to struggle with the beauty and symmetry of soccer ball fullerene–personal history
Haruo Hosoya
1
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_216b3ce453f595b56c4c00cfb540b5b6.pdf
eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2017-06-01
7
1
15
21
10.22061/jmns.2017.546
546
On the edge energy of some specific graphs
Saeid Alikhani
alikhani206@gmail.com
1
Fatemeh Mohebbi
2
Department of Mathematics, Yazd University, 89195-741, Yazd, Iran
Department of Mathematics, Yazd University, 89195-741, Yazd, Iran
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.
http://jmathnano.sru.ac.ir/article_546_f9c71ca1b8d4e4d48401276b55fec411.pdf
energy
edge energy
edge adjacency matrix
Line graph
eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2017-06-01
7
1
23
28
10.22061/jmns.2017.670
670
The second eccentric Zagreb index of the $N^{TH}$ growth of nanostar dendrimer $D_{3}[N]$
Mohammad Reza Farahani
mrfarahani88@gmail.com
1
Abdul Qudair Baig
aqbaig1@gmail.com
2
Wasim Sajjad
wasim.sajjad89@gmail.com
3
Department of Applied Mathematics, Iran University of Science and Technology (IUST), Narmak, Tehran 16844, Iran
Department of Mathematics, COMSATS Institute of Information Technology, Attock Campus, Pakistan
Department of Mathematics, University of Sargodha, Mandi Bahauddin Campus, Mandi Bahauddin Pakistan
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.
http://jmathnano.sru.ac.ir/article_670_2633e66e0388587817d173344152cf14.pdf
Molecular graph
Eccentricity
Zagreb topological index
nanostar dendrimer
D3[n]
eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2017-06-01
7
1
29
38
10.22061/jmns.2017.703
703
Strong chromatic index of certain nanosheets
Vidya Ganesan
vidyaganesan15@gmail.com
1
Indra Rajasingh
indrarajasingh@yahoo.com
2
School of Advanced Sciences
VIT University, Chennai-600127
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.
http://jmathnano.sru.ac.ir/article_703_7b6e3988c41ec6cc7c374883cff14757.pdf
strong edge-coloring
strong chromatic index
nanosheets
eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2017-06-01
7
1
39
60
10.22061/jmns.2017.705
705
On topological properties of boron triangular sheet BTS(m,n), borophene chain B36(n) and melem chain MC(n) nanostructures
Haidar Ali
haidar3830@gmail.com
1
Abdul Qudair Baig
aqbaig1@gmail.com
2
Muhammad Kashif Shafiq
kashif4v@gmail.com
3
Government College University Faisalabad Pakistan
Department of Mathematics, COMSATS Institute of Information Technology, Attock Campus, Pakistan
Department of Mathematics,Government College University, Faisalabad, Pakistan
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.
http://jmathnano.sru.ac.ir/article_705_5f1e113c297e2d34b446d432f8a75049.pdf
general Randic index
atom-bond connectivity ´ (ABC) index
geometric-arithmetic (GA) index
boron triangular
borophene
melem
eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2017-06-01
7
1
61
69
511
On the automorphism group of cubic polyhedral graphs
Mahin Songhori
1
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.
http://jmathnano.sru.ac.ir/article_511_f9cb2b06dcb533937e8e7a2d15076cc6.pdf
polyhedral graph
automorphism group
fullerene