A Hamiltonian graph is 2-factor Hamiltonian (2FH) if each of its 2-factors is a Hamiltonian
cycle. A similar, but weaker, property is the Perfect-Matching-Hamiltonian property (PMH …

A graph $ G $ has the Perfect-Matching-Hamiltonian property (PMH-property) if for each one
of its perfect matchings, there is another perfect matching of $ G $ such that the union of the …

Given a finite, simple, connected graph $ G=(V, E) $ with $| V|= n $, we consider the
associated graph Laplacian matrix $ L= DA $ with eigenvalues $0=\lambda_1<\lambda_2 …

A graph $ G $ has the\emph {Perfect Matching Hamiltonian property}(or for short, $ G $ is $
PMH $) if, for each one of its perfect matchings, there is another perfect matching of $ G …

Let G be a graph of even order, and consider KG as the complete graph on the same vertex
set as G. A perfect matching of KG is called a pairing of G. If for every pairing M of G it is …

令Q3DCq= Q1Q2··· Qq 为三维超立方体与圈的笛卡儿积图, Qi (1≤ i≤ q) 同构于Q3, M
为Q3DCq 的完美匹配. 依据每个Q3 中是否有点被连接两个Q3 的M 中边饱和, 把Q3DCq …