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

Abstract

In this paper we define extended corona and extended neighborhoodcorona of two graphs $G_{1}$ and $G_{2}$, which are denoted by$G_{1}\bullet G_{2}$ and $G_{1}\ast G_{2}$ respectively. Wecompute their adjacency spectrum, Laplacian spectrum and signlessLaplacian spectrum. As applications, we give methods to constructinfinite families of integral graphs, Laplacian integral graphsand expander graphs from known ones.

Keywords

• corona, integral graphs, energy of a graph, expander graphs