1. Simplified computation of matchings in polygraphsAnte Graovac, Damir Vukičević, Damir Ježek, Janez Žerovnik, 2005, izvirni znanstveni članek Opis: Matching polynomial and perfect matchings for fasciagraphs, rotagraphs and twisted rotagraphs are treated in the paper. Classical transfer matrix approach makes it possible to get recursions for matching polynomial and perfect matchings, but the order of the matrix grows exponentially in the number of the linking edges between monographs. Novel transfer matrices are introduced whose order is much lower than that in classical transfer matrices. The virtue of the method introduced is especially pronounced when twoor more linking edges end in the same terminal vertex of a monograph. An example of a polyacene polygraph with extended pairings is given where a novel matrix has only 16 entries as compared to 65536 entries in the classical transfer matrix. However, all pairings are treated here on equal footing, but the method introduced can be applied to selected types of pairings of interest in chemistry.
Ključne besede: polygraphs, matching polynomial, matchings, perfect matchings, Kekulé structures, extended structures, recursive enumeration, transfer matrix method
Objavljeno v DKUM: 05.07.2017; Ogledov: 1583; Prenosov: 93
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2. On algebraic and geometric Kekulé structures in benzenoid rotagraphsAnte Graovac, Damir Vukičević, Janez Žerovnik, 2006, izvirni znanstveni članek Opis: Recently introduced algebraic Kekulé structures (AKS) describe the ▫$\pi$▫-electron distribution within rings of a conjugated network. The ratio of the AKS countto the classical Kekulé structures count was studied in benzenoid rotagraphs. By considering three representative classes of such rotagraphs, it was shown that this ratio tends towards either 1 or 0, or its value lies between 0 and 1.
Ključne besede: Kekulé structures, Kekulé structure count, geometric and algebraic Kekulé structures, benzenoids, rotagraph
Objavljeno v DKUM: 05.07.2017; Ogledov: 1230; Prenosov: 102
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3. Binary coding of algebraic Kekulé structures of catacondensed benzenoid graphsDamir 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 v DKUM: 10.07.2015; Ogledov: 1256; Prenosov: 100
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4. 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, recenzija, prikaz knjige, kritika Ključne besede: matematika, kemijska teorija grafov, Kekuléjeve strukture, popolno prirejanje, mathematics, chemical graph theory, perfect matchings, Kekulé structures, capped zigzag nanotubes, chemistry
Objavljeno v DKUM: 10.07.2015; Ogledov: 1154; Prenosov: 43
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