剖分图上的拉普拉斯完美态转移

Laplacian Perfect State Transfer in Subdivision Graph

图G的剖分图S(G)是通过在图G的每条边中插入一个新的顶点而得到的图.本文研究了r正则图G(r≥2)的剖分图S(G)上的拉普拉斯完美态转移问题,证明了若r+1不是图G的拉普拉斯特征值,则S(G)不存在拉普拉斯完美态转移.

The subdivision graph S(G)of a graph is obtained by inserting a new vertex into each edge of G.In this paper,we investigate the existence of Laplacian perfect state transfer in the subdivision graph S(G)of an r-regular graph,with r≥2.We prove that if r+1 is not a Laplacian eigenvalue of an r-regular graph G,then there is no Laplacian perfect state transfer in S(G).