On the Laplacian spectra of some variants of corona

Among many graph operations corona of graphs is one of the well known graph operation which fascinates many researchers because of its beautiful graph structure. Subsequently, many variants of corona operation are defined and the spectral properties of these graphs have been studied. In this paper, we define two special forms of matrices namely: super corona matrix and super neighbourhood corona matrix. We describe all the eigenvalues and the corresponding eigenvectors of these matrices. Further, we define some more variants of corona graphs such as subdivision double corona, Q-graph double corona, R-graph double corona, total double corona, subdivision double neighbourhood corona, Q-graph double neighbourhood corona, R-graph double neighbourhood corona and total double neighbourhood corona. We give a complete description of the eigenvalues and the eigenvectors of graphs obtained under such operations with the help of the results obtained for super corona and super neighbourhood corona matrices.