Structural and spectral properties 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 seed graph, corona graphs are defined by taking corona product of the seed graph iteratively. We show that the cumulative degree distribution of corona graphs decay exponentially when the seed graph is regular and the cumulative betweenness distribution follows power law when the seed graph is a clique. We determine spectra and signless Laplacian spectra of corona graphs in terms of the corresponding spectra of the seed graph when the seed graph is regular or a complete bipartite graph. Laplacian spectra of corona graphs corresponding to any seed graph is obtained in terms of the Laplacian spectra of the seed graph.