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

Document Type : Research Paper


Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran.


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≥3 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.