Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
1
1-2
2011
06
01
On Zagreb indices of pseudo-regular graphs
1
12
EN
Tamas
Reti
Ivan
Gutman
gutman@kg.ac.rs
Damir
Vukicevic
10.22061/jmns.2011.458
Properties of the Zagreb indices of pseudo-regular graphs are established, with emphasis on the Zagreb indices inequality. The relevance of the results obtained for the theory of nanomolecules is pointed out.
http://jmathnano.sru.ac.ir/article_458.html
http://jmathnano.sru.ac.ir/article_458_4d741836e0e889fda39e63ff49ceedd0.pdf
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
1
1-2
2011
06
01
Szeged index of bipartite unicyclic graphs
13
24
EN
Hui
Dong
Department of Mathematics, South China Normal University
Guangzhou 510631, P.R. China
Bo
Zhou
Department of Mathematics, South China Normal University
Guangzhou 510631, P.R. China
10.22061/jmns.2011.459
The Szeged index of a connected graph G is defined as the sum of products n1(e|G)n2(e|G) over all edges e = uv of G where n1(e|G) and n2(e|G) are respectively the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u In this paper, we determine the n-vertex bipartite unicyclic graphs with the first, the second, the third and the fourth smallest Szeged indices.
Szeged index,unicyclic graphs,bipartite graphs,distance
http://jmathnano.sru.ac.ir/article_459.html
http://jmathnano.sru.ac.ir/article_459_7c055fc2546e6b7610e0573f3ce327ff.pdf
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
1
1-2
2011
06
01
Augmented eccentric connectivity index of single defect nanocones
25
31
EN
Tomislav
Doslic
Faculty of Civil Engineering, University of Zagreb, Kaciceva 26,
10000 Zagreb, CROATIA
doslic@grad.hr
Mahboobeh
Salehi
Department of Mathematics, Payame Noor University (PNU),
Aran&Bidgol, 87415141, I. R. Iran
10.22061/jmns.2011.460
We present explicit formulas for the values of augmented eccentric connectivity indices of single-defect nanocones. Our main result is that the augmented eccentricity index of an n-layer nanocone with a single k-gonal defect at its apex behaves asymptotically 27k(1- ln 2)n for k ≥ 5 .
Eccentricity,nanocone,Augmented eccentric connectivity index
http://jmathnano.sru.ac.ir/article_460.html
http://jmathnano.sru.ac.ir/article_460_d772ffc538c06bb0c6c565cfd2d4fe41.pdf
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
1
1-2
2011
06
01
Computing fifth geometric-arithmetic index for nanostar dendrimers
33
42
EN
Ante
Graovac
Institute R. Bošković, HR-10002 Zagreb, POB 180, Croatia, and Faculty of Science,
University of Split Nikole Tesle 12, HR-21000, Split, Croatia
Modjtaba
Ghorbani
Department of Mathematics, Faculty of Science, Shahid Rajaee
Teacher Training University, Tehran, 16785 – 136, I. R. Iran
mghorbani@srttu.edu
Mohammad Ali
Hosseinzadeh
10.22061/jmns.2011.461
The geometric-arithmetic index is a topological index was defined as GA(G)=∑uv2(dudv)1/2/(du+dv), in which degree of vertex u denoted by dG(u ). Now we define a new version of GA index as GA5(G)=∑uv2(δuδv)1/2/(δu+δv) , where δu=∑uvdv. The goal of this paper is to further the study of the GA5 index.
GA index,GA5 index,Dendrimers
http://jmathnano.sru.ac.ir/article_461.html
http://jmathnano.sru.ac.ir/article_461_6f99594dd12dde6fac71e18914631803.pdf
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
1
1-2
2011
06
01
Connective eccentric index of fullerenes
43
50
EN
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.2011.462
Fullerenes are carbon-cage molecules in which a number of carbon atoms are bonded in a nearly spherical configuration. The connective eccentric index of graph G is defined as C (G)= Σa V(G)deg(a)ε(a) -1, where ε(a) is defined as the length of a maximal path connecting a to another vertex of G. In the present paper we compute some bounds of the connective eccentric index and then we calculate this topological index for two infinite classes of fullerenes.
Connective eccentric index,eccentric connectivity index,Fullerene graphs
http://jmathnano.sru.ac.ir/article_462.html
http://jmathnano.sru.ac.ir/article_462_86570288c13a12d0bc40a9b2c501df0f.pdf
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
1
1-2
2011
06
01
Hosoya index and Fibonacci numbers
51
57
EN
Saeid
Alikhani
Department of Mathematics, Yazd University, 89195-741, Yazd, Iran
alikhani@yazduni.ac.ir
10.22061/jmns.2011.463
Let G =(V ,E) be a simple graph. The Hosoya index Z(G) of G is defined as the total number of edge independent sets of G . Fibonacci numbers are terms of the sequence defined in a quite simple recursive fashion. In this paper, we investigate the relationships between Hosoya index and Fibonacci numbers. Also we consider Fibonacci cubes and study some of its parameters which is related to Fibonacci numbers.
Hosoya index,Fibonacci number,Fibonacci cube
http://jmathnano.sru.ac.ir/article_463.html
http://jmathnano.sru.ac.ir/article_463_950607c0b986bf22dd9266dc3b925575.pdf
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
1
1-2
2011
06
01
The PI and vertex PI polynomial of dendimers
59
65
EN
Mohammad Ali
Salahshour
Department of Science, Islamic Azad University, Savadkooh Branch, Savadkooh,
Mazandaran, I. R. Iran
10.22061/jmns.2011.464
Let G be a simple connected graph. The vertex PI polynomial of G is defined as PIv(G ,x )=Σe=uv Xnu(e)+nv(e) here nu(e) is the number of vertices closer to u than v and nv(e) is the number of vertices closer to v than u. The PI polynomial of G is defined as PI(G ,x )=Σe=uv Xmu(e)+mv(e) , where mu(e) is the number of edges closer to u than v and mv(e) is the number of edges closer to v than u. In this paper, the PI and vertex PI polynomials of two types of dendrimers are computed.
PI polynomial,vertex PI polynomial,Szeged index
http://jmathnano.sru.ac.ir/article_464.html
http://jmathnano.sru.ac.ir/article_464_6a3c8d68d4c94d7d5d72c0967d7b0efe.pdf