1. Omega polynomial revisitedMircea V. Diudea, Sandi Klavžar, 2010, original scientific article Abstract: Omega polynomial was proposed by Diudea (Omega Polynomial, Carpath. J. Math., 2006, 22, 43-47) to count the opposite topologically parallel edges in graphs, particularly to describe the polyhedral nanostructures. In this paper, the main definitions are re-analyzed and clear relations with other three related polynomials are established. These relations are supported by close formulas and appropriate examples. Keywords: mathematics, chemical graph theory, counting polynomials, Ommega polynomial, Theta polynomial, Pi polynomial, PI index, Sadhana polynomial, Cluj-Ilmenau index, CI index Published in DKUM: 24.08.2017; Views: 1028; Downloads: 115 Full text (263,85 KB) This document has many files! More... |
2. Altered Wiener indicesDamir Vukičević, Janez Žerovnik, 2005, original scientific article Abstract: Recently Nikolić, Trinajstić and Randić put forward a novel modification ▫$^mW(G)$▫ of the Wiener number ▫$W(G)$▫, called modified Wiener index, which definition was generalized later by Gutman and the present authors. Here we study another class of modified indices defined as ▫$W_{min,λ}(G) = ∑(V(G)^λm_G(u,ν)^λ−m_G(u,ν)^{2λ})$▫ and show that some of the important properties of ▫$W(G)$▫, ▫$^mW(G)$▫ and ▫$^λW(G)$▫ are also properties of ▫$W_{min,λ}(G)$▫, valid for most values of the parameter λ. In particular, if ▫$T_n$▫ is any n-vertex tree, different from the n-vertex path ▫$P_n$▫ and the n-vertex star ▫$S_n$▫, then for any λ ≥ 1 or λ < 0, ▫$^W_{min,λ}(P_n) > W_{min,λ}(T_n)>W_{min,λ}(S_n)$▫. Thus for these values of the parameter λ, ▫$W_{min,λ}(G)$▫ provides a novel class of structure-descriptors, suitable for modeling branching-dependent properties of organic compounds, applicable in QSPR and QSAR studies. We also demonstrate that if trees are ordered with regard to ▫$W_{min,λ}(G)$▫ then, in the general case, this ordering is different for different λ. Keywords: mathematics, chemical graph theory, Wiener index, modified Wiener index Published in DKUM: 17.08.2017; Views: 1204; Downloads: 120 Full text (991,46 KB) This document has many files! More... |
3. Wiener numbers of pericondensed benzenoid hydrocarbonsSandi Klavžar, Ivan Gutman, Amal Rajapakse, 1997, original scientific article Abstract: Using a recently developed technique for the calculation of the Wiener number (W) of benzenoid systems, we determine explicit expressions for W for several homologous series of pericondensed benzenoid hydrocarbons. An elementary proof for the correctness of the used method is also included. Keywords: mathematics, chemical graph theory, distance in graphs, Wiener number, benzenoids Published in DKUM: 05.07.2017; Views: 1422; Downloads: 167 Full text (16,93 MB) This document has many files! More... |
4. Corroborating a modification of the Wiener indexIvan Gutman, Janez Žerovnik, 2002, other scientific articles Abstract: In a recent work [Chem. Phys. Lett. 333 (2001) 319-321] Nikolić, Trinajstić, and Randie put forward a novel modification ▫$^m$▫W of the Wiener index. We now show that ▫$^m$▫W possesses the basic properties required by a topological index to be acceptable as a measure of the extent of branching of the carbon-atom skeleton of the respective molecule (and therefore to be a structure-descriptor, potentially applicable in QSPR and QSAR studies). In particular, if ▫$T_n$▫ is any n-vertex tree, different from the n-vertex path ▫$P_n$▫ and the n-vertex star ▫$S_n$▫, then mw(Pn) < mW(Tn) < mW(Sn). We also show how the concept of the modified Wiener index can be extended to weighted molecular graphs. Keywords: graph theory, distance, molecular graphs, modified Wiener index, weigted modified Wiener index, branching, chemical graph theory Published in DKUM: 05.07.2017; Views: 1114; Downloads: 83 Full text (85,05 KB) This document has many files! More... |
5. Computing the Szeged indexJanez Žerovnik, 1996, original scientific article Abstract: We give an explicit algorithm for computing the Szeged index of a graph which runs in ▫$O(mn)$▫ time, where ▫$n$▫ is the number of nodes and ▫$m$▫ is the number of edges. Keywords: mathematics, chemistry, chemical graph theory, molecular graphs, structural formulae, algorithms, topological index, Szeged index Published in DKUM: 05.07.2017; Views: 1786; Downloads: 115 Full text (1,83 MB) This document has many files! More... |
6. A class of modified Wiener indicesIvan Gutman, Damir Vukičević, Janez Žerovnik, 2004, original scientific article Abstract: The Wiener index of a tree T obeys the relation W(T) = Σen1(e) • n2(e) where n1(e) and n2(e) are the number of vertices on the two sides of the edge e, and where the summation goes over all edges of T. Recently Nikolić, Trinajstić and Randić put forward a novel modification mW of the Wiener index, defined as mW(T) = Σe[n1(e) • n2(e)]–1. We now extend their definition as mWλ(T) = Σe[n1(e) • n2(e)]λ, and show that some of the main properties of both W and mW are, in fact, properties of mWλ, valid for all values of the parameter λ≠0. In particular, if Tn is any n-vertex tree, different from the n-vertex path Pn and the n-vertex star Sn, then for any positive λ, mWλ(Pn) > mWλ(Tn) > mWλ(Sn), whereas for any negative λ, mWλ(Pn) < mWλ(Tn) < mWλ(Sn). Thus mWλ provides a novel class of structure-descriptors, suitable for modeling branching-dependent properties of organic compounds, applicable in QSPR and QSAR studies. We also demonstrate that if trees are ordered with regard to mWλ then, in the general case, this ordering is different for different λ. Keywords: graph theory, chemical graph theory, modified Wiener index, Nikolić-Trinajstić-Randić index, branching Published in DKUM: 05.07.2017; Views: 1173; Downloads: 97 Full text (125,08 KB) This document has many files! More... |
7. Binary coding of algebraic Kekulé structures of catacondensed benzenoid graphsDamir Vukičević, Petra Žigert Pleteršek, 2008, original scientific article Abstract: Algebraična Kekuléjeva struktura končnega katakondenziranega benzenoidnega grafa s ▫$h$▫ šestkotniki je podana z binarno kodo dolžine ▫$h$▫. Postopek je obrnljiv in sicer lahko iz binarne kode rekonstruiramo algebraično Kekuléjevo strukturo. Keywords: matematika, kemijska teorija grafov, benzenoidni ogljikovodiki, benzenoidni grafi, Kekuléjeve strukture, Randićeve strukture, 1-faktor, binarno kodiranje, mathematics, chemical graph theory, benzenoid hydrocarbons, benzenoid graph, Kekulé structures, algebraic Kekulé structures, Randić structures, 1-factor, binary coding Published in DKUM: 10.07.2015; Views: 1223; Downloads: 98 Link to full text |
8. Li, Hao(PRC-TSI); Lu, Mei(PRC-TSI): The $m$-connectivity index of graphs. (English summary). - MATCH Commun. Math. Comput. Chem. 54 (2005), no. 2, 417--423.Sandi Klavžar, 2006, review, book review, critique Keywords: matematika, kemijska teorija grafov, lastna vrednost, Laplaceova matrika, utežen graf, mathematics, chemical graph theory, eigenvalue, Laplacian matrix, weighted graph Published in DKUM: 10.07.2015; Views: 37350; Downloads: 20 Link to full text |
9. Qian, Jianguo(PRC-XIAM-SM); Zhang, Fuji(PRC-XIAM-SM): On the number of Kekulé structures in capped zigzag nanotubes. (English summary). - J. Math. Chem. 38 (2005), no. 2, 233--246.Sandi Klavžar, 2006, review, book review, critique Keywords: matematika, kemijska teorija grafov, Kekuléjeve strukture, popolno prirejanje, mathematics, chemical graph theory, perfect matchings, Kekulé structures, capped zigzag nanotubes, chemistry Published in DKUM: 10.07.2015; Views: 1117; Downloads: 41 Link to full text |
10. Gutman, Ivan(YU-KRASC); Furtula, Boris(YU-KRASC); Toropov, Andrey A.; Toropova, Alla P.: The graph of atomic orbitals and its basic properties. II. Zagreb indices. (English summary). - MATCH Commun. Math. Comput. Chem. 53 (2005), no. 1, 225--230.Sandi Klavžar, 2005, review, book review, critique Keywords: matematika, kemijska teorija grafov, zaporedja stopenj točk, kemija, mathematics, chemical graph theory, degree sequences, chemistry Published in DKUM: 10.07.2015; Views: 937; Downloads: 24 Link to full text |