New Lower Bound on the Number of Perfect Matchings in Fullerene Graphs
By Heping Zhang, Fuji Zhang. 2001
52 citations recorded by the source corpus.
A fullerene graph is a cubic and 3-connected plane graph (or spherical map) that has exactly 12 faces of size 5 and other faces of size 6, which can be regarded as the molecular graph of a fullerene. T. Došlić [3] obtained that a fullerene graph with p vertices has at least (p+2)/2 perfect matchings by applying the recently developed decomposition techniques in matching theory of graphs. This note gets a better lower bound ⌈3(p+2)/4⌉ of the number of perfect matchings of a fullerene graph by finding its 2-extendability. This property further implies a chemical consequence that every derivative of a fullerene by substituting any two pairs of adjacent carbon atoms permits a Kekulé structure.
Subfields: Materials Chemistry, Organic Chemistry
View Paper: https://www.semanticscholar.org/paper/8d784f6015b9a8e9675973f0844adb92c7fe03c2
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In Materials Chemistry
In Organic Chemistry
Citations in the corpus
- Cyclical Edge-Connectivity of Fullerene Graphs and (k, 6)-Cages (2003, background): “Although the approach of [1] and [3] cannot be fully extended to the case of (k, 6)-cages, it may be worthwhile to follow it as far as it is possible.”
- Forcing on Perfect Matchings - A Survey (2011, background): “Zhang (2001) in [55], and the cyclically 5-edge-connectivity by Došlić (2003) in [10] and Qi and Zhang (2008) in [31].”