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Gluing Formula for the Pseudo-Determinant of Graph Laplacian and Applications to Counting of Spanning Trees

Shivjyot Brar, Sheng-Chang Chen, Sayonita Ghosh Hajra, Santosh Kandel

Source record

Source: arXiv

Published: Aug 26, 2026

arXiv: 2608.26458

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Source abstract

In this paper, we establish a gluing formula for the pseudo-determinant of the Laplacian on a simple finite graph. We achieve this by using the gluing formula for the determinant of massive Laplacian and the perturbation theory technique. In addition, we apply this gluing relation to derive a gluing formula for the number of spanning trees and rooted spanning forests on simple finite graphs.

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Gluing Formula for the Pseudo-Determinant of Graph Laplacian and Applications to Counting of Spanning Trees — Mathematical Frontier Network