Alkanes with Greatest Estrada Index
نویسندگان
چکیده
Several hundreds of so-called molecular structuredescriptors were proposed in the chemical literature [1] and are used for modeling of various physical and chemical properties of (mainly) organicmolecules. In general, a molecular structure-descriptor is a number, usually computed from the molecular graph [2, 3], that reflects certain topological features [4, 5] of the underlying molecule. Many of the currently used structure-descriptors quantify (and thus measure) a property of acyclic molecules that in chemistry is referred to as “branching” [6 – 10]. In connection with this, the question may be asked which are the most branched alkanes [11]. Recently this problem was examined in due detail [12]. It could be shown [12] that several molecular structure-descriptors imply that the most branched alkanes are those represented by the (below described) molecular graphs which we propose to be called Volkmann trees. It has been proven that Volkmann trees represent alkanes with a minimal Wiener index [13], and that these trees have the maximal greatest eigenvalue [14]. It was also empirically established [15] (but so far not proven) that Volkmann trees have the maximal greatest Laplacian eigenvalue [16, 17]. The reality of the existence of alkanes pertaining to Volkmann trees was tested by means of advanced quantum-chemical calculations [18]. In this paper we demonstrate that Volkmann trees are also the molecular graphs of alkanes with a maximal Estrada index.
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