  Given two graphs, a backbone and a finger, a comb product is a new graph
obtained by grafting a copy of the finger into each vertex of the backbone. We
study the comb graphs in the case when both components are the paths of order
$n$ and $k$, respectively, as well as the above comb graphs with an infinite
ray attached to some of their vertices. A detailed spectral analysis is carried
out in both situations.
