Spectra of some new extended corona

For two graphs \mathrm{G} and \mathrm{H} with n and m vertices, the corona \mathrm{G}\circ\mathrm{H} of \mathrm{G} and \mathrm{H} is the graph obtained by taking one copy of \mathrm{G} and n copies of \mathrm{H} and then joining the i^{th} vertex of \mathrm{G} to every vertex in the i^{th} copy of \mathrm{H}. The neighborhood corona \mathrm{G}\star\mathrm{H} of \mathrm{G} and \mathrm{H} is the graph obtained by taking one copy of \mathrm{G} and n copies of \mathrm{H} and joining every neighbor of the i^{th} vertex of \mathrm{G} to every vertex in the i^{th} copy of \mathrm{H}. In this paper, we define four new extensions of corona and neighborhood corona of two graphs \mathrm{G} and \mathrm{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 \mathrm{H} is a regular graph. As an application, we exhibit infinite families of integral graphs.

کلیدواژه ها:

spectrum ، corona ، neighborhood corona ، integral graphs