A class of gcd-graphs having Perfect State Transfer

doi:10.1016/j.endm.2016.05.027

Electronic Notes in Discrete Mathematics

Volume 53, September 2016, Pages 319-329

https://doi.org/10.1016/j.endm.2016.05.027 Get rights and content

Abstract

Let G be a graph with adjacency matrix A. The transition matrix corresponding to G is defined by $H (t) : = \exp (i t A), t \in R$ . The graph G is said to have perfect state transfer (PST) from a vertex u to another vertex v, if there exist $τ \in R$ such that the uv-th entry of $H (τ)$ has unit modulus. The graph G is said to be periodic at $τ \in R$ if there exist $γ \in C$ with $| γ | = 1$ such that $H (τ) = γ I$ , where I is the identity matrix. A gcd-graph is a Cayley graph over a finite abelian group defined by greatest common divisors. In this paper, we construct classes of gcd-graphs having periodicity and perfect state transfer.

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A class of gcd-graphs having Perfect State Transfer

Abstract

Linear Algebra and Its Applications

Discrete Mathematics

Integral Cayley Graphs

Characterization of circulant networks having perfect state transfer

Quantum inf. process

Quantum networks on cubelike graphs

Physical Review A