Signless Laplacian perfect state transfer in subdivision graph
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).
subdivision grapheigenvalueeigenvalue eigenvectorspectral decompositionperfect state transfer
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维普
