eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2012-06-01
2
1-2
1
8
10.22061/jmns.2012.465
465
The augmented eccentric connectivity index of nanotubes and nanotori
Suleyman Ediz
ediz571@gmail.com
1
Department of Mathematics, Yüzüncü Yıl University, Van 65080, Turkey
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.
http://jmathnano.sru.ac.ir/article_465_6c646b1105719b9fcfc9eb7c3ef4bba5.pdf
Augmented eccentric connectivity index
Nanotube
Nanotorus
eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2012-06-01
2
1-2
9
13
10.22061/jmns.2012.469
469
Hosoya index of bridge and splice graphs
Reza Sharafdini
sharafdini@gmail.com
1
Department of Mathematics, Faculty of Basic Sciences, Persian Gulf University, Bushehr 75169, Iran
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.
http://jmathnano.sru.ac.ir/article_469_99637a57bcb6d7df54ad31c6c5cec821.pdf
Hosoya index
bridge graphs
splices graphs
eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2012-06-01
2
1-2
15
20
10.22061/jmns.2012.466
466
A new version of Zagreb index of circumcoronene series of benzenoid
Mohammad Farahani
1
Department of Mathematics, Iran University of Science and Technology (IUST), Narmak, Tehran 16844, Iran
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.
http://jmathnano.sru.ac.ir/article_466_9149984141f8a7c65be493deecb18ae8.pdf
First Zagreb index
second Zagreb index
Fifth Zagreb index
Circumcoronene series of benzenoid
Cut Method
Ring-cut Method
eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2012-06-01
2
1-2
21
27
10.22061/jmns.2012.467
467
Eccentric connectivity index of fullerene graphs
Mahin Songhori
mahinsonghori@gmail.com
1
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785 – 136, I R. Iran
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.
http://jmathnano.sru.ac.ir/article_467_f95e4e880956234e6ae0bcc4a06407c9.pdf
eccentric connectivity index
eccentricity connectivity polynomial
fullerene
eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2012-06-01
2
1-2
29
36
10.22061/jmns.2012.468
468
Remarks on atom bond connectivity index
Somayyeh Nik-Andish
1
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785 – 136, I R. Iran
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.
http://jmathnano.sru.ac.ir/article_468_368201c77afa0785fc5c580c727b085c.pdf
atom bond connectivity index
matching
clique number
eng
Shahid Rajaee Teacher Training University
Journal of Mathematical Nanoscience
2538-2314
2538-2314
2012-06-01
2
1-2
37
41
10.22061/jmns.2012.470
470
A note on eccentric distance sum
Mahin Songhori
mahinsonghori@gmail.com
1
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785 – 136, I R. Iran
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
http://jmathnano.sru.ac.ir/article_470_5c72a2c52ae3749775af6e0a3a4b6986.pdf
eccentricity
eccentric distance sum
Volkmann tree