Cliques and the spectral radius

We prove a number of relations between the number of cliques of a graph G and the largest eigenvalue @m(G) of its adjacency matrix. In particular, writing k"s(G) for the number of s-cliques of G, we show that, for all r>=2,@m^r^+^1(G)= =(@m(G)n-1+1r)r(r-1)r+1(nr)^r^+^1.

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