Spectra of extended neighborhood corona and extended corona of two graphs

Abstract

In this paper we define extended corona and extended neighborhood corona of two graphs G1 and G2, which are denoted by G1 • G2 and G1 * G2 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.