eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2011-06-01
1
1-2
1
12
10.22061/jmns.2011.458
458
On Zagreb indices of pseudo-regular graphs
Tamas Reti
1
Ivan Gutman
gutman@kg.ac.rs
2
Damir Vukicevic
3
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_4d741836e0e889fda39e63ff49ceedd0.pdf
eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2011-06-01
1
1-2
13
24
10.22061/jmns.2011.459
459
Szeged index of bipartite unicyclic graphs
Hui Dong
1
Bo Zhou
2
Department of Mathematics, South China Normal University Guangzhou 510631, P.R. China
Department of Mathematics, South China Normal University Guangzhou 510631, P.R. China
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.
http://jmathnano.sru.ac.ir/article_459_7c055fc2546e6b7610e0573f3ce327ff.pdf
Szeged index
unicyclic graphs
bipartite graphs
distance
eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2011-06-01
1
1-2
25
31
10.22061/jmns.2011.460
460
Augmented eccentric connectivity index of single defect nanocones
Tomislav Doslic
doslic@grad.hr
1
Mahboobeh Salehi
2
Faculty of Civil Engineering, University of Zagreb, Kaciceva 26, 10000 Zagreb, CROATIA
Department of Mathematics, Payame Noor University (PNU), Aran&Bidgol, 87415141, I. R. Iran
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 .
http://jmathnano.sru.ac.ir/article_460_d772ffc538c06bb0c6c565cfd2d4fe41.pdf
eccentricity
nanocone
Augmented eccentric connectivity index
eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2011-06-01
1
1-2
33
42
10.22061/jmns.2011.461
461
Computing fifth geometric-arithmetic index for nanostar dendrimers
Ante Graovac
1
Modjtaba Ghorbani
mghorbani@srttu.edu
2
Mohammad Ali Hosseinzadeh
3
Institute R. Bošković, HR-10002 Zagreb, POB 180, Croatia, and Faculty of Science, University of Split Nikole Tesle 12, HR-21000, Split, Croatia
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785 – 136, I. R. Iran
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.
http://jmathnano.sru.ac.ir/article_461_6f99594dd12dde6fac71e18914631803.pdf
GA index
GA5 index
Dendrimers
eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2011-06-01
1
1-2
43
50
10.22061/jmns.2011.462
462
Connective eccentric index of fullerenes
Modjtaba Ghorbani
mghorbani@srttu.edu
1
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785 – 136, I. R. Iran
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.
http://jmathnano.sru.ac.ir/article_462_86570288c13a12d0bc40a9b2c501df0f.pdf
Connective eccentric index
eccentric connectivity index
Fullerene graphs
eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2011-06-01
1
1-2
51
57
10.22061/jmns.2011.463
463
Hosoya index and Fibonacci numbers
Saeid Alikhani
alikhani@yazduni.ac.ir
1
Department of Mathematics, Yazd University, 89195-741, Yazd, Iran
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.
http://jmathnano.sru.ac.ir/article_463_950607c0b986bf22dd9266dc3b925575.pdf
Hosoya index
Fibonacci number
Fibonacci cube
eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2011-06-01
1
1-2
59
65
10.22061/jmns.2011.464
464
The PI and vertex PI polynomial of dendimers
Mohammad Ali Salahshour
1
Department of Science, Islamic Azad University, Savadkooh Branch, Savadkooh, Mazandaran, I. R. Iran
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.
http://jmathnano.sru.ac.ir/article_464_6a3c8d68d4c94d7d5d72c0967d7b0efe.pdf
PI polynomial
vertex PI polynomial
Szeged index