Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2
1-2
2012
06
01
The augmented eccentric connectivity index of nanotubes and nanotori
1
8
EN
Suleyman
Ediz
Department of Mathematics, Yüzüncü Yıl University, Van 65080, Turkey
ediz571@gmail.com
10.22061/jmns.2012.465
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.
Augmented eccentric connectivity index,Nanotube,Nanotorus
http://jmathnano.sru.ac.ir/article_465.html
http://jmathnano.sru.ac.ir/article_465_6c646b1105719b9fcfc9eb7c3ef4bba5.pdf
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2
1-2
2012
06
01
Hosoya index of bridge and splice graphs
9
13
EN
Reza
Sharafdini
Department of Mathematics, Faculty of Basic Sciences, Persian Gulf University,
Bushehr 75169, Iran
sharafdini@gmail.com
10.22061/jmns.2012.469
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.
Hosoya index,bridge graphs,splices graphs
http://jmathnano.sru.ac.ir/article_469.html
http://jmathnano.sru.ac.ir/article_469_99637a57bcb6d7df54ad31c6c5cec821.pdf
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2
1-2
2012
06
01
A new version of Zagreb index of circumcoronene series of benzenoid
15
20
EN
Mohammad
Farahani
Department of Mathematics, Iran University of Science and Technology (IUST),
Narmak, Tehran 16844, Iran
10.22061/jmns.2012.466
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 $M_1(G)=sum_{uvin E}d_u+d_v$ and $M_1(G)=sum_{uvin E}d_ud_v$, where du denotes the degree of vertex u in G. Recently, we know new versions of Zagreb indices as $M_1^{*}(G)=sum_{uvin E}ecc(u)+ecc(v)$, $M_1^{**}(G)=sum_{uin V}ecc(u)^2$ and $M_2^{*}(G)=sum_{uvin E}ecc(u)ecc(v)$, 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.
First Zagreb index,second Zagreb index,Fifth Zagreb index,Circumcoronene series of benzenoid,Cut Method,Ring-cut Method
http://jmathnano.sru.ac.ir/article_466.html
http://jmathnano.sru.ac.ir/article_466_9149984141f8a7c65be493deecb18ae8.pdf
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2
1-2
2012
06
01
Eccentric connectivity index of fullerene graphs
21
27
EN
Mahin
Songhori
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training
University, Tehran, 16785 – 136, I R. Iran
mahinsonghori@gmail.com
10.22061/jmns.2012.467
The eccentric connectivity index of the molecular graph is defined as $zeta^c(G)=sum_{uvin E}degG(u)ε(u)$ , 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.
eccentric connectivity index,eccentricity connectivity polynomial,fullerene
http://jmathnano.sru.ac.ir/article_467.html
http://jmathnano.sru.ac.ir/article_467_f95e4e880956234e6ae0bcc4a06407c9.pdf
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2
1-2
2012
06
01
Remarks on atom bond connectivity index
29
36
EN
Somayyeh
Nik-Andish
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University,
Tehran, 16785 – 136, I R. Iran
10.22061/jmns.2012.468
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.
atom bond connectivity index,matching,clique number
http://jmathnano.sru.ac.ir/article_468.html
http://jmathnano.sru.ac.ir/article_468_368201c77afa0785fc5c580c727b085c.pdf
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2
1-2
2012
06
01
A note on eccentric distance sum
37
41
EN
Mahin
Songhori
Department of Mathematics, Faculty of Science, Shahid Rajaee
Teacher Training University, Tehran, 16785 – 136, I R. Iran
mahinsonghori@gmail.com
10.22061/jmns.2012.470
The eccentric distance sum is a graph invariant defined as $sum_{uvin E} εG(v)DG(v)$, 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
Eccentricity,eccentric distance sum,Volkmann tree
http://jmathnano.sru.ac.ir/article_470.html
http://jmathnano.sru.ac.ir/article_470_5c72a2c52ae3749775af6e0a3a4b6986.pdf