Computing the spectrum of L^t(G) for a regular graph

If L(G) is the line graph of G, it is difficult to get the adjacency matrix of Lt(G)=L(L(L ... L(G))); t≥۳ and also its spectrum. In this paper, we present a formula to compute the spectrum of Lt(G), for each positive integer t, where G is a regular graph.

Keywords:

Line graph , Simple graph , Adjacency matrix , Eigenvalue of a matrix , Characteristic polynomial , Spectra of a graph