The Laplacian and distance matrix of a signed tree
نویسندگان
1 MOE-LCSM, CHP-LCOCS, School of Mathematics and Statistics, Hunan Normal University Changsah, China
2 MOE-LCSM, CHP-LCOCS, School of Mathematics and Statistics, Hunan Normal University Changsah, China
3 MOE-LCSM, CHP-LCOCS, School of Mathematics and Statistics, Hunan Normal University Changsah, China
doi
10.22108/toc.2025.137241.2061چکیده
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.
