The (normalized) Laplacian Spectrum And State Transition Of The Crown Operation Of The Graph

The spectra of graph is an important branch of graph theory,which is widely applied in physical,chemistry and computer science.This paper mainly focuses on the corona of graphs,and studies the normalized Laplacian spectra of the double coronae based on R-graphs and the signless Laplacian quantum state transfer based on corona.The main content of this paper consists of two parts:In the first part:we completely characterize the normalized Laplacian spectra of the double coronae based on R-graphs,R-vertex corona and R-edge corona,when factor graphs are regular.Furthermore,we apply the above results to construct infinitely many pairs of normalized Laplacian cospectral graphs.In the second part:we explore some conditions that guarantee the signless Laplacian perfect state transfer,and show that there is no perfect state transfer for some special graphs.In addition,it is proved that G o Km has no signless Laplacian perfect state transfer for some special m.For any regular graph H,??? H has signless Laplacian pretty good state transfer but no perfect state transfer.??? K₁ has signless Laplacian pretty good state transfer,where nK₂ is the cocktail party graph.