The Laplacian and distance matrix of a signed tree

Articles in Press

Document Type : Research Paper

Authors

MOE-LCSM, CHP-LCOCS, School of Mathematics and Statistics, Hunan Normal University Changsah, China

10.22108/toc.2025.137241.2061

Abstract

Let $N$ and $\widetilde{D}$ be net Laplacian and net distance matrices of a signed tree, respectively. The inverse (resp. group inverse) of $\widetilde{D}$ is obtained if it is nonsingular (resp. singular), which extend the inverse formula obtained by Graham and Lov'{a}sz for distance matrix of a unsigned tree. The interlacing inequality connecting the eigenvalues of $\widetilde{D}$ and $N$ of a signed tree is also obtained.

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References

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Transactions on Combinatorics

Articles in Press, Corrected Proof
Available Online from 13 July 2025

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History

  • Receive Date: 02 April 2023
  • Revise Date: 19 May 2025
  • Accept Date: 29 May 2025
  • Published Online: 13 July 2025

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