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Squared Distance Matrix Of A Weighted Tree, Ravindra B. Bapat

Journal Articles

Let T be a tree with vertex set f1;: :: ; ng such that each edge is assigned a nonzero weight. The squared distance matrix of T; denoted by 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 A formula for 1 is also obtained, under certain conditions. The results generalize known formulas for the unweighted case.