Perfect state transfer in NEPS of some graphs
Shasha Zheng, Xiaogang Liu, Shenggui Zhang · Linear and Multilinear Algebra · 2018
Let G be a graph with adjacency matrix AG. The transition matrix of G corresponding to AG is denoted as HAG(t):=exp(−itAG) (t∈R, i=−1). If there is some time τ∈R such that HAG(τ)u,v has unit modulus, where u and v are distinct vertices in G, then we say that G admits perfect state transfer from u to v. In this paper, we first show that a non-complete extended p-sum (NEPS) with badly decomposed factors has no perfect state transfer. And then, we prove that NEPS of a cube with odd distance has perfect state transfer when the sum of elements in its basis is not zero and that NEPS of a cube with even distance exhibits perfect state transfer if and only if there is a tuple in the basis such that it has exact one coordinate which is valued 1.