NDLI: Distributive lattice structure on the set of perfect matchings of carbon nanotubes

Content Provider	Springer Nature Link
Author	Tratnik, Niko Žigert Pleteršek, Petra
Copyright Year	2016
Abstract	Carbon nanotubes are composed of carbon atoms linked in hexagonal shapes, with each carbon atom covalently bonded to three other carbon atoms. Carbon nanotubes have diameters as small as 1 nm and lengths up to several centimeters. Carbon nanotubes can be open-ended or closed-ended (fullerenes). Open-ended single-walled carbon nanotubes are also called tubulenes. The resonance graph R(T) of a tubulene T reflects interactions between Kekulé structures—i.e. perfect matchings of T. With the orientation of edges the resonance digraph $$\overrightarrow{R}(T)$$ of a tubulene is obtained. As the main result we show that $$\overrightarrow{R}(T)$$ is isomorphic to the Hasse diagram of the direct sum of some distributive lattices. Similar results were proved in [10, 16], but one can not directly apply them to tubulenes. As a consequence of the main result it is proved that every connected component of R(T) is a median graph. Further we show that the block graph of every connected component H of the resonance graph of a tubulene is a path and that H contains at most two vertices of degree one.
Starting Page	1296
Ending Page	1305
Page Count	10
File Format	PDF
ISSN	02599791
Journal	Journal of Mathematical Chemistry
Volume Number	54
Issue Number	6
e-ISSN	15728897
Language	English
Publisher	Springer International Publishing
Publisher Date	2016-03-09
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Carbon nanotube Kekulé structure Resonance graph Distributive lattice Median graph Block graph Physical Chemistry Theoretical and Computational Chemistry Math. Applications in Chemistry
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Chemistry

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