2019-02-23T13:21:46Z
http://jmathnano.sru.ac.ir/?_action=export&rf=summon&issue=110
Journal of Mathematical Nanoscience
J. Math. Nanosci.
2012
2
1-2
The augmented eccentric connectivity index of nanotubes and nanotori
Suleyman
Ediz
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
2012
06
01
1
8
http://jmathnano.sru.ac.ir/article_465_6c646b1105719b9fcfc9eb7c3ef4bba5.pdf
Journal of Mathematical Nanoscience
J. Math. Nanosci.
2012
2
1-2
Hosoya index of bridge and splice graphs
Reza
Sharafdini
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
2012
06
01
9
13
http://jmathnano.sru.ac.ir/article_469_99637a57bcb6d7df54ad31c6c5cec821.pdf
Journal of Mathematical Nanoscience
J. Math. Nanosci.
2012
2
1-2
A new version of Zagreb index of circumcoronene series of benzenoid
Mohammad
Farahani
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
2012
06
01
15
20
http://jmathnano.sru.ac.ir/article_466_9149984141f8a7c65be493deecb18ae8.pdf
Journal of Mathematical Nanoscience
J. Math. Nanosci.
2012
2
1-2
Eccentric connectivity index of fullerene graphs
Mahin
Songhori
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
2012
06
01
21
27
http://jmathnano.sru.ac.ir/article_467_f95e4e880956234e6ae0bcc4a06407c9.pdf
Journal of Mathematical Nanoscience
J. Math. Nanosci.
2012
2
1-2
Remarks on atom bond connectivity index
Somayyeh
Nik-Andish
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
2012
06
01
29
36
http://jmathnano.sru.ac.ir/article_468_368201c77afa0785fc5c580c727b085c.pdf
Journal of Mathematical Nanoscience
J. Math. Nanosci.
2012
2
1-2
A note on eccentric distance sum
Mahin
Songhori
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
2012
06
01
37
41
http://jmathnano.sru.ac.ir/article_470_5c72a2c52ae3749775af6e0a3a4b6986.pdf