Bounds on graph eigenvalues II Original Research Article

We prove three results about the spectral radius μ(G) of a graph G: (a) Let Tr(n) be the r-partite Turán graph of order n. If G is a Kr+1-free graph of order n, thenμ(G)<μ(Tr(n))unless G=Tr(n). (b) For most irregular graphs G of order n and size m,μ(G)-2m/n>1/(2m+2n). (c) Let 0less-than-or-equals, slantkless-than-or-equals, slantl. If G is a graph of order n with no image and no K2,l+1, thenimage