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

Abstract

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