Perfect state transfer in NEPS of some graphs. Issue 8 (2nd August 2020)

• Record Type: Journal Article
• Authors: Zheng, Shasha; Liu, Xiaogang; Zhang, Shenggui
• Is Part Of: Linear & multilinear algebra. Volume 68:Issue 8(2020)
• Page Start: 1518
• Page End: 1533
• Publication Date: 2020-08-02
• Subjects: Perfect state transfer -- NEPS of graphs -- badly decomposed graph -- cube; 05C50 -- 81P68 -- 15A18; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2018.1548555
• Languages: English
• ISSNs: 0308-1087

Abstract

ABSTRACT: Let G be a graph with adjacency matrix A G . The transition matrix of G corresponding to A G is denoted as H A G ( t ) := exp ⁡ ( − i t A G ) ( t ∈ R, i = − 1 ) . If there is some time τ ∈ R such that H A G ( 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.