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