Bounds on graph eigenvalues II

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)1/(2m+2n).(c)Let 0⩽k⩽l. If G is a graph of order n with no K2+K¯k+1 and no K2,l+1, thenμ(G)⩽minG),(k-l+1+(k-l+1)2+4l(n-1))/2}.