Work place: School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo Henan, 454000, China

E-mail: yanfeima2022@163.com

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Biography

Yanfei Ma is currently pursuing a master's degree at the School of Mathematics and Information Science of Henan Polytechnic University in China. Her research interests are graph theory and its applications.

DOI: https://doi.org/10.5815/ijmsc.2023.03.01, Pub. Date: 8 Aug. 2023

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. DošliÄ‡ 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

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