The augmented eccentric connectivity index of nanotubes and nanotori
Suleyman
Ediz
Department of Mathematics, Yüzüncü Yıl University, Van 65080, Turkey
author
text
article
2012
eng
Let G be a connected graph, the augmented eccentric connectivity index is a topological index was defined as $\zeta(G)=\sum_{i=1}^nM_i/E_i$, where Mi is the product of degrees of all vertices vj, adjacent to vertex vi, Ei is the largest distance between vi and any other vertex vk of G or the eccentricity of i v and n is the number of vertices in graph G. In this paper exact formulas for the augmented eccentric connectivity index of TUC4C8(S) nanotube and TC4C8(R) nanotorus are given.
Journal of Mathematical Nanoscience
Shahid Rajaee Teacher Training University
2538-2314
2
v.
1-2
no.
2012
1
8
http://jmathnano.sru.ac.ir/article_465_6c646b1105719b9fcfc9eb7c3ef4bba5.pdf
dx.doi.org/10.22061/jmns.2012.465
Hosoya index of bridge and splice graphs
Reza
Sharafdini
Department of Mathematics, Faculty of Basic Sciences, Persian Gulf University,
Bushehr 75169, Iran
author
text
article
2012
eng
The Hosoya index of a graph is defined as the total number of the matchings (including the empty edge set) of the graph. In this paper, explicit formulas are given for the Hosoya index of bridge and splice graphs.
Journal of Mathematical Nanoscience
Shahid Rajaee Teacher Training University
2538-2314
2
v.
1-2
no.
2012
9
13
http://jmathnano.sru.ac.ir/article_469_99637a57bcb6d7df54ad31c6c5cec821.pdf
dx.doi.org/10.22061/jmns.2012.469
A new version of Zagreb index of circumcoronene series of benzenoid
Mohammad
Farahani
Department of Mathematics, Iran University of Science and Technology (IUST),
Narmak, Tehran 16844, Iran
author
text
article
2012
eng
Among topological indices, Zagreb indices are very important, very old and they have many useful properties in chemistry and specially in mathematics chemistry. First and second Zagreb indices have been introduced by Gutman and Trinajstić as $M_1(G)=\sum_{uv\in E}d_u+d_v$ and $M_1(G)=\sum_{uv\in E}d_ud_v$, where du denotes the degree of vertex u in G. Recently, we know new versions of Zagreb indices as $M_1^{*}(G)=\sum_{uv\in E}ecc(u)+ecc(v)$, $M_1^{**}(G)=\sum_{u\in V}ecc(u)^2$ and $M_2^{*}(G)=\sum_{uv\in E}ecc(u)ecc(v)$, where ecc(u) is the largest distance between u and any other vertex v of G. In this paper, we focus one of these new topological indices that we call fifth Zagreb index $M_2^*(G)=M_5(G)$ and we compute this index for a famous molecular graph Circumcoronene series of benzenoid Hk, k≥ 1.
Journal of Mathematical Nanoscience
Shahid Rajaee Teacher Training University
2538-2314
2
v.
1-2
no.
2012
15
20
http://jmathnano.sru.ac.ir/article_466_9149984141f8a7c65be493deecb18ae8.pdf
dx.doi.org/10.22061/jmns.2012.466
Eccentric connectivity index of fullerene graphs
Mahin
Songhori
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training
University, Tehran, 16785 – 136, I R. Iran
author
text
article
2012
eng
The eccentric connectivity index of the molecular graph is defined as $\zeta^c(G)=\sum_{uv\in E}degG(u)ε(u)$ , where degG(x) denotes the degree of the vertex x in G and ε(u)=max{d(x,u) |x ε V(G)}. In this paper this polynomial is computed for an infinite class of fullerenes.
Journal of Mathematical Nanoscience
Shahid Rajaee Teacher Training University
2538-2314
2
v.
1-2
no.
2012
21
27
http://jmathnano.sru.ac.ir/article_467_f95e4e880956234e6ae0bcc4a06407c9.pdf
dx.doi.org/10.22061/jmns.2012.467
Remarks on atom bond connectivity index
Somayyeh
Nik-Andish
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University,
Tehran, 16785 – 136, I R. Iran
author
text
article
2012
eng
A topological index is a function Top from Σ into real numbers with this property that Top(G) = Top(H), if G and H are isomorphic. Nowadays, many of topological indices were defined for different purposes. In the present paper we present some properties of atom bond connectivity index.
Journal of Mathematical Nanoscience
Shahid Rajaee Teacher Training University
2538-2314
2
v.
1-2
no.
2012
29
36
http://jmathnano.sru.ac.ir/article_468_368201c77afa0785fc5c580c727b085c.pdf
dx.doi.org/10.22061/jmns.2012.468
A note on eccentric distance sum
Mahin
Songhori
Department of Mathematics, Faculty of Science, Shahid Rajaee
Teacher Training University, Tehran, 16785 – 136, I R. Iran
author
text
article
2012
eng
The eccentric distance sum is a graph invariant defined as $\sum_{uv\in E} εG(v)DG(v)$, where εG(v) is the eccentricity of a vertex v in G and DG(v ) is the sum of distances of all vertices in G from v. In this paper, we compute the eccentric distance sum of Volkmann tree and then we obtain some results for vertex−transitive graphs
Journal of Mathematical Nanoscience
Shahid Rajaee Teacher Training University
2538-2314
2
v.
1-2
no.
2012
37
41
http://jmathnano.sru.ac.ir/article_470_5c72a2c52ae3749775af6e0a3a4b6986.pdf
dx.doi.org/10.22061/jmns.2012.470