Real state transfer on edge perturbed graphs with generalised clusters

We study the existence of real state transfer in edge-perturbed graphs having generalised clusters, where the Hamiltonian is taken to be either the adjacency matrix, the Laplacian matrix, or the signless Laplacian matrix associated with a weighted graph. This approach establishes a unified framework for constructing new graphs exhibiting perfect real state transfer by leveraging known examples with this property. The results presented herein generalise several previously established findings on real state transfer. In particular, we construct an infinite family of graphs with maximum valency five that exhibit perfect pair state transfer with respect to each of the aforementioned matrices, between the same pair states and at the same transfer time, despite the fact that these graphs are not regular.