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The Laplacian and distance matrix of a signed tree | ||
| Transactions on Combinatorics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 08 خرداد 1404 | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2025.137241.2061 | ||
| نویسندگان | ||
| Hou Yaoping* 1؛ Hong Zixuan2؛ Xiong Zhuan2 | ||
| 1Department of Mathematics Hunan Normal University Changsha, Hunan,410081 | ||
| 2School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. 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 | ||
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آمار تعداد مشاهده مقاله: 12 |
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