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Let G be a graph with adjacency matrix A, let H(t) = exp(itA). G is called a periodic graph if there exists a time τ such that H(τ) is diagonal. If u and v are distinct vertices in G, we say that perfect state transfer occurs from u to v if there exists a time τ such that |H(τ) u,v | = 1. A necessary and sufficient condition for G is periodic is given. We… (More)

Let G be a connected graph of order n. The resistance matrix of G is defined as R G = (r ij (G)) n×n , where r ij (G) is the resistance distance between two vertices i and j in G. Eigenvalues of R G are called R-eigenvalues of G. If all row sums of R G are equal, then G is called resistance-regular. For any connected graph G, we show that R G determines the… (More)

For a k-uniform hypergraph H, we obtain some trace formulas for the Laplacian tensor of H, which imply that n i=1 d s i (s = 1,. .. , k) is determined by the Laplacian spectrum of H, where d 1 ,. .. , d n is the degree sequence of H. Using trace formulas for the Laplacian tensor, we obtain expressions for some coefficients of the Laplacian polynomial of a… (More)