کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4598769 | 1631104 | 2016 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Squared distance matrix of a tree: Inverse and inertia
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Squared distance matrix of a tree: Inverse and inertia Squared distance matrix of a tree: Inverse and inertia](/preview/png/4598769.png)
چکیده انگلیسی
Let T be a tree with vertices V(T)={1,…,n}V(T)={1,…,n}. The distance between vertices i,j∈V(T)i,j∈V(T), denoted dijdij, is defined to be the length (the number of edges) of the path from i to j . We set dii=0,i=1,…,ndii=0,i=1,…,n. The squared distance matrix Δ of T is the n×nn×n matrix with (i,j)(i,j)-element equal to 0 if i=ji=j, and dij2 if i≠ji≠j. It is known that Δ is nonsingular if and only if the tree has at most one vertex of degree 2. We obtain a formula for Δ−1Δ−1, if it exists. When the tree has no vertex of degree 2, the formula is particularly simple and depends on a certain “two-step” Laplacian of the tree. We determine the inertia of Δ. The inverse and the inertia of the edge orientation matrix are also described.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 491, 15 February 2016, Pages 328–342
Journal: Linear Algebra and its Applications - Volume 491, 15 February 2016, Pages 328–342
نویسندگان
R.B. Bapat, Sivaramakrishnan Sivasubramanian,