Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 1 1-2 2011 06 01 On Zagreb indices of pseudo-regular graphs 1 12 458 10.22061/jmns.2011.458 EN Tamas Reti Ivan Gutman Damir Vukicevic Journal Article 2011 01 22 Properties of the Zagreb indices of pseudo-regular graphs are established, with emphasis on the Zagreb indices inequality. The relevance of the results obtained for the theory of nanomolecules is pointed out. https://jdma.sru.ac.ir/article_458_4d741836e0e889fda39e63ff49ceedd0.pdf

Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 1 1-2 2011 06 01 Szeged index of bipartite unicyclic graphs 13 24 459 10.22061/jmns.2011.459 EN Hui Dong Department of Mathematics, South China Normal University Guangzhou 510631, P.R. China Bo Zhou Department of Mathematics, South China Normal University Guangzhou 510631, P.R. China Journal Article 2011 01 10 The Szeged index of a connected graph G is defined as the sum of products n₁(e|G)n₂(e|G) over all edges e = uv of G where n₁(e|G) and n₂(e|G) are respectively the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u In this paper, we determine the n-vertex bipartite unicyclic graphs with the first, the second, the third and the fourth smallest Szeged indices. https://jdma.sru.ac.ir/article_459_7c055fc2546e6b7610e0573f3ce327ff.pdf

Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 1 1-2 2011 06 01 Augmented eccentric connectivity index of single defect nanocones 25 31 460 10.22061/jmns.2011.460 EN Tomislav Doslic Faculty of Civil Engineering, University of Zagreb, Kaciceva 26, 10000 Zagreb, CROATIA Mahboobeh Salehi Department of Mathematics, Payame Noor University (PNU), Aran&Bidgol, 87415141, I. R. Iran Journal Article 2011 01 05 We present explicit formulas for the values of augmented eccentric connectivity indices of single-defect nanocones. Our main result is that the augmented eccentricity index of an n-layer nanocone with a single k-gonal defect at its apex behaves asymptotically 27k(1- ln 2)n for k ≥ 5 . https://jdma.sru.ac.ir/article_460_d772ffc538c06bb0c6c565cfd2d4fe41.pdf

Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 1 1-2 2011 06 01 Computing fifth geometric-arithmetic index for nanostar dendrimers 33 42 461 10.22061/jmns.2011.461 EN Ante Graovac Institute R. Bošković, HR-10002 Zagreb, POB 180, Croatia, and Faculty of Science, University of Split Nikole Tesle 12, HR-21000, Split, Croatia Modjtaba Ghorbani Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785 – 136, I. R. Iran Mohammad Ali Hosseinzadeh Journal Article 2011 01 03 The geometric-arithmetic index is a topological index was defined as GA(G)=∑_uv2(d_ud_v)^1/2/(d_u+d_v), in which degree of vertex u denoted by d_G(u ). Now we define a new version of GA index as GA₅(G)=∑_uv2(δ_uδ_v)^1/2/(δ_u+δ_v) ,  where δ_{u=∑_uv}d_v. The goal of this paper is to further the study of the GA₅ index. https://jdma.sru.ac.ir/article_461_6f99594dd12dde6fac71e18914631803.pdf

Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 1 1-2 2011 06 01 Connective eccentric index of fullerenes 43 50 462 10.22061/jmns.2011.462 EN Modjtaba Ghorbani Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785 – 136, I. R. Iran Journal Article 2011 01 16 Fullerenes are carbon-cage molecules in which a number of carbon atoms are bonded in a nearly spherical configuration. The connective eccentric index of graph G is defined as C (G)= Σ_{a V(G)}deg(a)ε(a)^-1, where ε(a) is defined as the length of a maximal path connecting a to another vertex of G. In the present paper we compute some bounds of the connective eccentric index and then we calculate this topological index for two infinite classes of fullerenes. https://jdma.sru.ac.ir/article_462_86570288c13a12d0bc40a9b2c501df0f.pdf

Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 1 1-2 2011 06 01 Hosoya index and Fibonacci numbers 51 57 463 10.22061/jmns.2011.463 EN Saeid Alikhani Department of Mathematics, Yazd University, 89195-741, Yazd, Iran Journal Article 2011 01 03 Let G =(V ,E) be a simple graph. The Hosoya index Z(G) of G is defined as the total number of edge independent sets of G . Fibonacci numbers are terms of the sequence defined in a quite simple recursive fashion. In this paper, we investigate the relationships between Hosoya index and Fibonacci numbers. Also we consider Fibonacci cubes and study some of its parameters which is related to Fibonacci numbers. https://jdma.sru.ac.ir/article_463_950607c0b986bf22dd9266dc3b925575.pdf

Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 1 1-2 2011 06 01 The PI and vertex PI polynomial of dendimers 59 65 464 10.22061/jmns.2011.464 EN Mohammad Ali Salahshour Department of Science, Islamic Azad University, Savadkooh Branch, Savadkooh, Mazandaran, I. R. Iran Journal Article 2011 01 03 Let G be a simple connected graph. The vertex PI polynomial of G is defined as PI_v(G ,x )=Σ_e=uv X^{n_u(e)+<span>n</span>_v<span>(e) </span>}here <span>n</span>_u<span>(e)</span> is the number of vertices closer to u than v and <span>n</span>_v<span>(e)</span> is the number of vertices closer to v than u. The PI polynomial of G is defined as  PI(G ,x )=Σ_e=uv X^{m_u(e)+m_v(e)} , where <span>m</span>_u<span>(e)</span> is the number of edges closer to u than v and <span>m</span>_v<span>(e)</span> is the number of edges closer to v than u. In this paper, the PI and vertex PI polynomials of two types of dendrimers are computed. https://jdma.sru.ac.ir/article_464_6a3c8d68d4c94d7d5d72c0967d7b0efe.pdf