On the distance matrix of a tree |
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| Authors: | M Edelberg MR Garey RL Graham |
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| Institution: | Department of Electrical Engineering, Princeton University, Princeton, N.J. 08540, USA;Bell Laboratories, Murray Hill, N.J. 07974, USA |
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| Abstract: | For a tree T on n vertices, let D(T)=(dij) denote the distance matrix of T, i.e., dij(T) is just the length of the unique path then the ith vertex and the jth vertex of T. Denote by ΔT(x) the characteristic polynom, of D(T), so that ΔT(x) = det(D(T) xl). In this paper, we investigate a number of properties of ΔT(x). In particular, we find simple expressions for the first few and last few coefficients of ΔT(x). |
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