Spectra of Some New Extended Corona

For two graphs g and h with n and m vertices, the corona g o h of g and h is the graph obtained by taking one copy of g and n copies of h and then joining the ith vertex of g to every vertex in the ith copy of h. the neighborhood corona g ⋆ h of g and h is the graph obtained by taking one copy of g and n copies of h and joining every neighbor of the ith vertex of g to every vertex in the ith copy of h. in this paper, we define four new extensions of corona and neighborhood corona of two graphs g and h; named the identity-extended corona, identity-extended neighborhood corona, neighborhood extended corona and neighborhood extended neighborhood corona and then determine the spectrum of their adjacency matrix, where h is a regular graph. as an application, we exhibit infinite families of integral graphs.