Spectra of the extended neighborhood corona and extended corona of two graphs

<p>In this paper we define extended corona and extended neighborhood<br />corona of two graphs $G_{1}$ and $G_{2}$, which are denoted by<br />$G_{1}\bullet G_{2}$ and $G_{1}\ast G_{2}$ respectively. We<br />compute their adjacency spectrum, Laplacian spectrum and signless<br />Laplacian spectrum. As applications, we give methods to construct<br />infinite families of integral graphs, Laplacian integral graphs<br />and expander graphs from known ones.