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1.
Omega polynomial revisited
Mircea V. Diudea, Sandi Klavžar, 2010, izvirni znanstveni članek

Opis: 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.
Ključne besede: mathematics, chemical graph theory, counting polynomials, Ommega polynomial, Theta polynomial, Pi polynomial, PI index, Sadhana polynomial, Cluj-Ilmenau index, CI index
Objavljeno: 24.08.2017; Ogledov: 404; Prenosov: 66
.pdf Celotno besedilo (263,85 KB)
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2.
Altered Wiener indices
Damir Vukičević, Janez Žerovnik, 2005, izvirni znanstveni članek

Opis: 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.
Ključne besede: mathematics, chemical graph theory, Wiener index, modified Wiener index
Objavljeno: 17.08.2017; Ogledov: 470; Prenosov: 77
.pdf Celotno besedilo (991,46 KB)
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3.
Wiener numbers of pericondensed benzenoid hydrocarbons
Sandi Klavžar, Ivan Gutman, Amal Rajapakse, 1997, izvirni znanstveni članek

Opis: 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.
Ključne besede: mathematics, chemical graph theory, distance in graphs, Wiener number, benzenoids
Objavljeno: 05.07.2017; Ogledov: 637; Prenosov: 120
.pdf Celotno besedilo (16,93 MB)
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4.
Corroborating a modification of the Wiener index
Ivan Gutman, Janez Žerovnik, 2002, kratki znanstveni prispevek

Opis: 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.
Ključne besede: graph theory, distance, molecular graphs, modified Wiener index, weigted modified Wiener index, branching, chemical graph theory
Objavljeno: 05.07.2017; Ogledov: 507; Prenosov: 57
.pdf Celotno besedilo (85,05 KB)
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5.
Computing the Szeged index
Janez Žerovnik, 1996, izvirni znanstveni članek

Opis: 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.
Ključne besede: mathematics, chemistry, chemical graph theory, molecular graphs, structural formulae, algorithms, topological index, Szeged index
Objavljeno: 05.07.2017; Ogledov: 705; Prenosov: 81
.pdf Celotno besedilo (1,83 MB)
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6.
A class of modified Wiener indices
Ivan Gutman, Damir Vukičević, Janez Žerovnik, 2004, izvirni znanstveni članek

Opis: 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.
Ključne besede: graph theory, chemical graph theory, modified Wiener index, Nikolić-Trinajstić-Randić index, branching
Objavljeno: 05.07.2017; Ogledov: 555; Prenosov: 80
.pdf Celotno besedilo (125,08 KB)
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7.
Binary coding of algebraic Kekulé structures of catacondensed benzenoid graphs
Damir Vukičević, Petra Žigert Pleteršek, 2008, izvirni znanstveni članek

Opis: 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.
Ključne besede: 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
Objavljeno: 10.07.2015; Ogledov: 653; Prenosov: 77
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