2018-12-11T06:56:17Z
http://jmathnano.sru.ac.ir/?_action=export&rf=summon&issue=109
Journal of Mathematical Nanoscience
J. Math. Nanosci.
2011
1
1-2
On Zagreb indices of pseudo-regular graphs
Tamas
Reti
Ivan
Gutman
Damir
Vukicevic
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.
2011
06
01
1
12
http://jmathnano.sru.ac.ir/article_458_4d741836e0e889fda39e63ff49ceedd0.pdf
Journal of Mathematical Nanoscience
J. Math. Nanosci.
2011
1
1-2
Szeged index of bipartite unicyclic graphs
Hui
Dong
Bo
Zhou
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
2011
06
01
13
24
http://jmathnano.sru.ac.ir/article_459_7c055fc2546e6b7610e0573f3ce327ff.pdf
Journal of Mathematical Nanoscience
J. Math. Nanosci.
2011
1
1-2
Augmented eccentric connectivity index of single defect nanocones
Tomislav
Doslic
Mahboobeh
Salehi
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
2011
06
01
25
31
http://jmathnano.sru.ac.ir/article_460_d772ffc538c06bb0c6c565cfd2d4fe41.pdf
Journal of Mathematical Nanoscience
J. Math. Nanosci.
2011
1
1-2
Computing fifth geometric-arithmetic index for nanostar dendrimers
Ante
Graovac
Modjtaba
Ghorbani
Mohammad Ali
Hosseinzadeh
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
2011
06
01
33
42
http://jmathnano.sru.ac.ir/article_461_6f99594dd12dde6fac71e18914631803.pdf
Journal of Mathematical Nanoscience
J. Math. Nanosci.
2011
1
1-2
Connective eccentric index of fullerenes
Modjtaba
Ghorbani
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
2011
06
01
43
50
http://jmathnano.sru.ac.ir/article_462_86570288c13a12d0bc40a9b2c501df0f.pdf
Journal of Mathematical Nanoscience
J. Math. Nanosci.
2011
1
1-2
Hosoya index and Fibonacci numbers
Saeid
Alikhani
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
2011
06
01
51
57
http://jmathnano.sru.ac.ir/article_463_950607c0b986bf22dd9266dc3b925575.pdf
Journal of Mathematical Nanoscience
J. Math. Nanosci.
2011
1
1-2
The PI and vertex PI polynomial of dendimers
Mohammad Ali
Salahshour
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
2011
06
01
59
65
http://jmathnano.sru.ac.ir/article_464_6a3c8d68d4c94d7d5d72c0967d7b0efe.pdf