Séminaire Lotharingien de Combinatoire, 93B.50 (2025), 12 pp.
Harry Richman, Farbod Shokrieh and Chenxi Wu
Principal Minors of Tree Distance Matrices (Extended Abstract)
Abstract.
Suppose D is the distance matrix of a tree.
Graham and Pollack showed that the determinant of D satisfies a surprising identity
that depends only on the number of vertices in the given tree.
We generalize this result to a combinatorial identity for the determinant of
any principal submatrix of D.
This new identity involves counts of spanning forests and is proved by use of potential-theoretic concepts on graphs.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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