The subdivision graph S(G)of a graph is a graph obtained by inserting a new vertex into each edge of G.In order to solve the problem of perfect state subdivision graph.Using the spectral decomposition form of signless Laplacian matrix of subdivision graph,this paper investigated the existence of signless Laplacian perfect state transfer in the subdivision graph S(G)of an r-regular graph,where r≥2.Obtained the signless Laplacian eigenvalues and corresponding eigenprojections for subdivision graphs of regular graphs,the results showed that if r-1 was not signles Laplacian eigenvalue of an graph G,then there was no signless Laplacian perfect state transfer in S(G).
关键词
剖分图/特征值/特征向量/谱分解/完美态转移
Key words
subdivision graph/eigenvalue/eigenvalue eigenvector/spectral decomposition/perfect state transfer
维普
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