  Coalescing involves gluing one or more rooted graphs onto another graph.
Under specific conditions, it is possible to start with cospectral graphs that
are coalesced in similar ways that will result in new cospectral graphs. We
present a sufficient condition for this based on the block structure of
similarity matrices, possibly with additional constraints depending on which
type of matrix is being considered. The matrices considered in this paper
include the adjacency, Laplacian, signless Laplacian, distance, and generalized
distance matrix.
