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 theexistence 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).
关键词
剖分图/拉普拉斯特征值/拉普拉斯完美态转移
Key words
subdivision graph/Laplacian eigenvalue/Laplacian perfect state transfer
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