کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9498231 | 1631200 | 2005 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On distance matrices and Laplacians
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
We consider distance matrices of certain graphs and of points chosen in a rectangular grid. Formulae for the inverse and the determinant of the distance matrix of a weighted tree are obtained. Results concerning the inertia and the determinant of the distance matrix of an unweighted unicyclic graph are proved. If D is the distance matrix of a tree, then we obtain certain results for a perturbation of Dâ1. As an example, it is shown that if Lâ¼ is the Laplacian matrix of an arbitrary connected graph, then D-1-Lâ¼-1 is an entrywise positive matrix. We consider the distance matrix of a subset of a rectangular grid of points in the plane. If we choose m + k â 1 points, not containing a closed path, in an m Ã k grid, then a formula for the determinant of the distance matrix of such points is obtained.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 401, 15 May 2005, Pages 193-209
Journal: Linear Algebra and its Applications - Volume 401, 15 May 2005, Pages 193-209
نویسندگان
R. Bapat, S.J. Kirkland, M. Neumann,