Let C(p) be the caterpillar obtained from the stars S(p1+1), S(p2+1) , ... , S(pd+i) +1 and the path P(d-1) by identifying the root ofS(pi+1) with the i-vertex of P(d-1). The line graph of C(p), denoted by 12,(C(p)), becomes a sequence of cliques K(p1+1), K(p2+2), ... , Kp(d-2+2), K(pd-1+1) in this order, such that two consecutive cliques have in common exactly one vertex. In this paper, we characterize the eigenvalues and the energy of L(C(p)). Explicit formulas are given for the eigenvalues and the energy of L(C(a)) where a = vertical bar a, a, ... , a vertical bar. Finally, a lower bound and an upper bound for the energy of C(C(p)) are derived. (C) 2011 Elsevier Inc. All rights reserved.