Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
4
1-2
2014
06
01
On the spectrum of Cayley graphs via character table
1
11
EN
Farzaneh
Nowroozi
Department of Mathematics, Faculty of Science, Shahid RajaeeTeacher Training University, Tehran, 16785 – 136, I R. Iran
Modjtaba
Ghorbani
Department of Mathematics, Faculty of Science, Shahid RajaeeTeacher Training University, Tehran, 16785 – 136, I R. Iran
mghorbani@srttu.edu
10.22061/jmns.2014.477
A Cayley graph can be consider as an interpretation of group representation. This means that one can construct the Cayley graph Г = Cay(G, S) by having the vertex set to be the elements of G with g~h if and only if hg-1 ε S. In this paper, we focus our attention on Cayley graphs with a normal symmetric subset. We also determine all eigenvalues of Buckminster fullerene by constructing Cay(G,S) where G is the alternating group A5.
eigenvalue,Cayley graph,characteristic polynomial
http://jmathnano.sru.ac.ir/article_477.html
http://jmathnano.sru.ac.ir/article_477_166922038b274bc7128566c1e2ce4b98.pdf
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
4
1-2
2014
06
01
Augmented eccentric connectivity index of Fullerenes
13
18
EN
Reza
Sharafdini
Department of Mathematics, Faculty of Science, Persian Gulf University
sharafdini@gmail.com
10.22061/jmns.2014.478
Fullerenes are carbon-cage molecules in which a number of carbon atoms are bonded in a nearly spherical configuration. The augmented eccentric connectivity index of graph G is defined as £(G)=∑u εV(G)M(u)ε(u)-1, where ε(u) is defined as the length of a maximal path connecting u to another vertex of G and M(u) denotes the product of degrees of all eighbors of vertex u. In the present paper , we compute the augmented eccentric connectivity index of two classes of fullerenes C12n+2 and C20n+40.
Augmented eccentric connectivity index,Eccentricity,Fullerene graphs
http://jmathnano.sru.ac.ir/article_478.html
http://jmathnano.sru.ac.ir/article_478_800b8677745303e8ee086eaa27425650.pdf
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
4
1-2
2014
06
01
Differences between Wiener and modified Wiener indices
19
25
EN
Mardjan
Hakimi-Nezhaad
Department of Mathematics, Faculty of Science, Shahid Rajaee
Teacher Training University, Tehran, 16785 – 136, I R. Iran
m_hakimi20@yahoo.com
Modjtaba
Ghorbani
Department of Mathematics, Faculty of Science, Shahid Rajaee
Teacher Training University, Tehran, 16785 – 136, I R. Iran
mghorbani@srttu.edu
10.22061/jmns.2014.479
The Wiener index is the oldest topological index introduced by H. Wiener for anticipating the boiling point of Paraffin and some other alkenes. An algebraic approach for generalizing the Wiener index is proposed by Graovac and Pisanski for the first time. In this paper, we compute the difference between these topological indices for a class of fullerene graphs.
Wiener index,Molecular graph,automorphism of graph
http://jmathnano.sru.ac.ir/article_479.html
http://jmathnano.sru.ac.ir/article_479_3b5f1f807f52f598f7054c36fd451058.pdf
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
4
1-2
2014
06
01
Computing the energy of small fullerenes
27
36
EN
Tayebeh
Ghorbani
Institute of Nanoscience and Nanotechnology, University of Kashan,
8731751167 Kashan, I. R Iran
10.22061/jmns.2014.481
The concept of energy of graph is defined in 1978 by Ivan Gutman as the sum of the absolute values of the eigenvalues of a graph. In this article we estimate the energy of small fullerenes.
eigenvalue,fullerene,graph energy
http://jmathnano.sru.ac.ir/article_481.html
http://jmathnano.sru.ac.ir/article_481_ad953d6c600cc97fbb128a5a439ce631.pdf
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
4
1-2
2014
06
01
On the Zagreb indices of overfull molecular graphs
37
44
EN
Maryam
Jalali-Rad
Department of Pure Mathematics, Faculty of Mathematical Sciences,
University of Kashan, Kashan, I. R. Iran
10.22061/jmns.2014.482
Let G be a connected graph on n vertices. An overfull graph is a graph whose number of its edges is greater than Δ × [n/2], where Δ is the maximum degree of vertices in G. In this paper, we compute the Zagreb indices of overfull molecular graphs.
overfull graph,Zagreb indices,Molecular graph
http://jmathnano.sru.ac.ir/article_482.html
http://jmathnano.sru.ac.ir/article_482_989e2f8c1e53a06f95bc290282b465f4.pdf
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
4
1-2
2014
06
18
Spectral properties of some matrices related to topological indices
45
50
EN
Samaneh
Zangi
Department of Mathematics, Faculty of Science, Shahid Rajaee
Teacher Training University, Tehran, 16785 – 136, I R. Iran
10.22061/jmns.2014.668
A topological index is a kind of molecular descriptor which anticipates some properties of chemical compound. The aim of this paper is to compute the spectrum of PA adjacency matrix associated to a well-known topological index.
spectrum of graph,Topological index,adjacency matrix
http://jmathnano.sru.ac.ir/article_668.html
http://jmathnano.sru.ac.ir/article_668_e939142adc188a0351eb71391bf9ea23.pdf