A class of gcd-graphs having Perfect State Transfer
| Autor: | Hiranmoy Pal, Bikash Bhattacharjya |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Vertex (graph theory)
Cayley graph Applied Mathematics Identity matrix Stochastic matrix 010103 numerical & computational mathematics 0102 computer and information sciences 01 natural sciences Graph Combinatorics 010201 computation theory & mathematics FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Combinatorics (math.CO) Adjacency matrix 0101 mathematics Abelian group Perfect state transfer Mathematics |
| Zdroj: | Electronic Notes in Discrete Mathematics. 53:319-329 |
| ISSN: | 1571-0653 |
| DOI: | 10.1016/j.endm.2016.05.027 |
| Popis: | 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 ∈ R . The graph G is said to have perfect state transfer (PST) from a vertex u to another vertex v, if there exist τ ∈ R such that the uv-th entry of H ( τ ) has unit modulus. The graph G is said to be periodic at τ ∈ R if there exist γ ∈ 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. |
| Databáze: | OpenAIRE |
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