研究了r-正则图G(r ≥ 2)的剖分图S(G)上的完美态传递问题,并证明了当λs+r(0 ≤ s ≤ d)是一个非完全平方数时,则S(G)的任意两个顶点之间不存在完美态传递.
Perfect State Transfer in Subdivision Graph
Let G a simple undirected and connected r-regular graph of n order,λ0＞λ1＞…＞λd is all the distinct eigenvalues of its adjacency matrix.The subdivision graph S(G)of a graph G is a graph obtained by inserting a new vertex into each edge of G.In this paper,we investigate the existence of perfect state transfer in the subdivision graph S(G)of an r-regular graph,wherer≥2.It is proved that if λs+r(0≤s ≤d)is a square-free integers,then there is no perfect state transfer between any two vertices in S(G).
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维普
