The normalized Laplacian and related indexes of graphs with edges blew up by cliques
Abstract
In this paper, we introduce the clique-blew up graph CL(G) of a given graph G, which is obtained from G by replacing each edge of G with a complete graph Kn. We characterize all the normalized Laplacian spectrum of the grpah CL(G) in term of the given graph G. Based on the spectrum obtained, the formulae to calculate the multiplicative degree-Kirchhoff index, the Kemeny's constant and the number of spanning trees of CL(G) are derived well. Finally, the spectrum and indexes of the clique-blew up iterative graphs are present.
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