The Laplacian and distance matrix of a signed tree

Zixuan, Hong; Yaoping, Hou; Zhuan, Xiong

doi:10.22108/toc.2025.137241.2061

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	The Laplacian and distance matrix of a signed tree
Transactions on Combinatorics
دوره 15، شماره 2، شهریور 2026، صفحه 111-124 اصل مقاله (488.79 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2025.137241.2061
نویسندگان
Hong Zixuan؛ Hou Yaoping^* ؛ Xiong Zhuan
MOE-LCSM, CHP-LCOCS, School of Mathematics and Statistics, Hunan Normal University Changsah, China
چکیده
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.
کلیدواژه‌ها
signed tree؛ net distance matrix؛ net Laplacian matrix؛ group inverse

مراجع
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The Laplacian and distance matrix of a signed tree