On Spectra of Corona Graphs

Abstract

Product graphs have been gainfully used in literature to generate mathematical models of complex networks which inherit properties of real networks. Realizing the duplication phenomena imbibed in the definition of corona product of two graphs, we define corona graphs. Given a small simple connected graph which we call basic graph, corona graphs are defined by taking corona product of the basic graph iteratively. We calculate the possibility of having a node of degree k in any corona graph which lead to obtain degree distribution of corona graphs. We determine explicit formulae of eigenvalues, Laplacian eigenvalues and signless Laplacian eigenvalues of corona graphs when the basic graph is regular. Computable expressions of eigenvalues and signless Laplacian eigenvalues are also obtained when the basic graph is a star graph.