Shahid Rajaee Teacher Training UniversityJournal of Mathematical Nanoscience2538-231421-220120601The augmented eccentric connectivity index of nanotubes and nanotori1846510.22061/jmns.2012.465ENSuleymanEdizDepartment of Mathematics, Yüzüncü Yıl University, Van 65080, TurkeyJournal Article20111104Let 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 v<sub>j</sub>, adjacent to vertex v<sub>i</sub>, E<sub>i</sub> is the largest distance between vi and any other vertex v<sub>k</sub> 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.https://jmathnano.sru.ac.ir/article_465_6c646b1105719b9fcfc9eb7c3ef4bba5.pdfShahid Rajaee Teacher Training UniversityJournal of Mathematical Nanoscience2538-231421-220120601Hosoya index of bridge and splice graphs91346910.22061/jmns.2012.469ENRezaSharafdiniDepartment of Mathematics, Faculty of Basic Sciences, Persian Gulf University,
Bushehr 75169, IranJournal Article20120110The 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.https://jmathnano.sru.ac.ir/article_469_99637a57bcb6d7df54ad31c6c5cec821.pdfShahid Rajaee Teacher Training UniversityJournal of Mathematical Nanoscience2538-231421-220120601A new version of Zagreb index of circumcoronene series of benzenoid152046610.22061/jmns.2012.466ENMohammadFarahaniDepartment of Mathematics, Iran University of Science and Technology (IUST),
Narmak, Tehran 16844, IranJournal Article20111005Among 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 H<sub>k</sub>, k≥ 1.https://jmathnano.sru.ac.ir/article_466_9149984141f8a7c65be493deecb18ae8.pdfShahid Rajaee Teacher Training UniversityJournal of Mathematical Nanoscience2538-231421-220120601Eccentric connectivity index of fullerene graphs212746710.22061/jmns.2012.467ENMahinSonghoriDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training
University, Tehran, 16785 – 136, I R. IranJournal Article20120105The eccentric connectivity index of the molecular graph is defined as $\zeta^c(G)=\sum_{uv\in E}deg<sub>G</sub>(u)ε(u)$ , where deg<sub>G</sub>(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.https://jmathnano.sru.ac.ir/article_467_f95e4e880956234e6ae0bcc4a06407c9.pdfShahid Rajaee Teacher Training UniversityJournal of Mathematical Nanoscience2538-231421-220120601Remarks on atom bond connectivity index293646810.22061/jmns.2012.468ENSomayyehNik-AndishDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University,
Tehran, 16785 – 136, I R. IranJournal Article20110906A 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.https://jmathnano.sru.ac.ir/article_468_368201c77afa0785fc5c580c727b085c.pdfShahid Rajaee Teacher Training UniversityJournal of Mathematical Nanoscience2538-231421-220120601A note on eccentric distance sum374147010.22061/jmns.2012.470ENMahinSonghoriDepartment of Mathematics, Faculty of Science, Shahid Rajaee
Teacher Training University, Tehran, 16785 – 136, I R. IranJournal Article20111204The eccentric distance sum is a graph invariant defined as $\sum_{uv\in E} ε<sub>G</sub>(v)D<sub>G</sub>(v)$, where ε<sub>G</sub>(v) is the eccentricity of a vertex v in G and D<sub>G</sub>(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 graphshttps://jmathnano.sru.ac.ir/article_470_5c72a2c52ae3749775af6e0a3a4b6986.pdf