Perfect state transfer in neighborhood coronas

Abstract

The neighborhood corona $G\star H$ is the graph obtained by taking one copy $G$ and $|G|$ copies of $H$, and joining each vertex of the $j$th copy of $H$ to all neighbors of $v_j$ in $G$. In this paper, we study the state transfer of neighborhood coronas related to the adjacency matrix. Concretely, we provide some necessary conditions under which the neighborhood corona $G\star H$ admits perfect state transfer, and obtain a new family of graphs with pretty good state transfer based on neighborhood coronas.

16 pages, 1 figures. arXiv admin note: text overlap with arXiv:1605.05260 by other authors