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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Ravindra B. Bapat
Indian Statistical Institute, New Delhi, 110016, India
Electrical & Electronics Engineering

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Squared distance matrix of a weighted tree Ravindra B. Bapat
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 7, No 2 (2019): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2019.7.2.8

Abstract

Let T be a tree with vertex set {1, …, n} such that each edge is assigned a nonzero weight. The squared distance matrix of T,  denoted by Δ,  is the n × n matrix with (i, j)-element d(i, j)2,  where d(i, j) is the sum of the weights of the edges on the (ij)-path. We obtain a formula for the determinant of Δ. A formula for Δ − 1 is also obtained, under certain conditions. The results generalize known formulas for the unweighted case.
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