Abstract：Two special properties of graphs are studied in this paper. Both of these properties are stable. Firstly， the closure operation is carried out on the original graph and the closure of the original graph is constructed. Whether the original graph has some property is transformed into the complement of the closure. Secondly， the structure of the complement of closure is reasonably classified and discussed. Finally， it is found that under certain conditions the independent number of the original graph is no more than k when the signless Laplacian spectral radius of the complement is not greater than 2k， or under certain conditions， the original graph is Hamilton-connected when the signless Laplacian spectral radius of the complement is not greater than n－2.
2022, Vol. 56 
