  For d-regular graph G, an edge-signing sigma:E(G) \rightarrow {-1,1} is
called a good signing if the absolute eigenvalues of adjacency matrix are at
most 2 \sqrt{d-1}. Bilu-Linial conjectured that for each regular graph there
exists a good signing. In this paper, by using new concept "Equitable
Partition", we solve the Bilu-Linial Conjecture for some cases. We show that
how to find out a good signing for special complete graphs and lexicographic
product of two graphs. In particular, if there exist two good signings for
graph G, then we can find a good signing for a 2-lift of G.
