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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 d1, . . . , dn 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)
The group inverses of block matrices have numerous applications in many areas, such as singular differential and difference equations, Markov chains, iterative methods, cryptography and so on (see [1–6]). In 1979, Campbell and Meyer proposed an open problem to find an explicit representation for the Drazin inverse of a 2 2 block matrix A B C D , where the… (More)
Let G be a weighted graph with Laplacian matrix L and signless Laplacian matrix Q. In this note, block representations for the group inverse of L and Q are given. The resistance distance in a graph can be obtained from the block representation of the group inverse of L.
For a cycle Cn , let Cn ◦ 2K1 be the graph obtained from Cn by attaching two pendant edges to each vertex of Cn . In this paper, we prove that Cn ◦ 2K1 is determined by its signless Laplacian spectrum when n = 32, 64. We also show that Cn ◦ 2K1 is determined by its Laplacian spectrum.
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)