IJMSC Vol. 9, No. 3, 8 Aug. 2023

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Fullerene Graph, Tubular Fullerene, Perfect Matching, Cyclic Edge-cut

The perfect matchings counting problem of graphs has important applications in combinatorial optimization, statistical physics, quantum chemistry and other fields. A perfect matching of a graph *G* is a set of non-adjacent edges that covers all vertices of *G* . The number of perfect matchings of a graph is closely related to its number of vertices. A fullerene graph is a 3-connected cubic planar graphs all of whose faces are pentagons and hexagons. Došlić obtained that a fullerene graph with *P* vertices has at least P/2+1 perfect matchings, Zhang et al. proved a better lower bound 3(*p*+2)/4 of the number of perfect matchings of a fullerene graph. We have known that the fullerene graph has a nontrivial cyclic 5-edge-cut if and only if it is isomorphic to the graph *T _{n}* for some integer n >=1, where

Yanfei Ma, Rui Yang, "On the number of Perfect Matchings of Tubular Fullerene Graphs", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.9, No.3, pp. 1-11, 2023. DOI:10.5815/ijmsc.2023.03.01

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