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

Chandrashekar Adiga (Department of Studies in Mathematics, University of Mysore, Manasagangothri, Mysuru - 570 006, India)
Rakshith B.R. (Department of Studies in Mathematics, University of Mysore, Manasagangothri, Mysuru - 570 006, India)
Subba Krishna K.N. (Department of Studies in Mathematics, University of Mysore, Manasagangothri, Mysuru - 570 006, India)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 4, No 1 (2016): Electronic Journal of Graph Theory and Applications

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.