Real State Transfer On Edge Perturbed Graphs with Generalised Clusters

Abstract

We study the existence of real state transfer [1, 2] in edge-perturbed graphs containing generalized clusters, where the Hamiltonian is taken to be either the adjacency matrix, the Laplacian matrix, or the signless Laplacian matrix of an associated weighted graph. This framework provides a unified approach for constructing new graphs that exhibit perfect real state transfer, building on known examples with this property. In particular, we construct an infinite family of non-regular graphs with maximum valency five that exhibit perfect pair state transfer—under all three matrices—between the same pair of states at the same time. We further identify examples of perfect pair state transfer in certain edge-perturbed graphs and graph products.