On Schatten p-norm of the distance matrices of graphs (Journal Article)

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Abstract: For a connected simple graph G, the generalized distance matrix is defined by, where Tr(G) is the diagonal matrix of vertex transmissions and D(G) is the distance matrix. For particular values of
, we obtain the distance matrix, the distance Laplacian matrix and the distance signless Laplacian matrix and other uncountable distance based matrices. Let be the eigenvalues of G and a real number, the Schatten p-norm is the p-th root of the sum of p-th powers of eigenvalues of, that is. In this paper, we obtain various bounds for in terms of different graph parameters and characterize the corresponding extremal graphs.