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New Lower Bound on the Number of Perfect Matchings in Fullerene Graphs

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Lanzhou University, Lanzhou, Gansu, 730000, P.R. China

    Heping Zhang & Fuji Zhang

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  1. Heping Zhang
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  2. Fuji Zhang
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Zhang, H., Zhang, F. New Lower Bound on the Number of Perfect Matchings in Fullerene Graphs. Journal of Mathematical Chemistry 30, 343–347 (2001). https://doi.org/10.1023/A:1015131912706

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