کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8897802 | 1631043 | 2018 | 16 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Upper bound for the trace norm of the Laplacian matrix of a digraph and normally regular digraphs
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Upper bound for the trace norm of the Laplacian matrix of a digraph and normally regular digraphs Upper bound for the trace norm of the Laplacian matrix of a digraph and normally regular digraphs](/preview/png/8897802.png)
چکیده انگلیسی
The trace norm of MâMn(C) is defined as âMââ=âk=1nÏk, where Ï1â¥Ï2â¥â¯â¥Ïnâ¥0 are the singular values of M (i.e. the square roots of the eigenvalues of MMâ). We are particularly interested in the trace norm âL(D)âanInââ, where L(D) is the Laplacian matrix of a digraph D with n vertices and a arcs, and In is the nÃn identity matrix. When D=G is a graph with n vertices and m edges, then âL(D)âanInââ=âL(G)â2mnInââ=LE(G), the Laplacian energy of G introduced by Gutman and Zhou in 2006. We show that for a digraph D with n vertices and a arcs,âL(D)âanInâââ¤n(aâa2n+âi=1n(di+)2), where d1+,â¦,dn+ are the outer degrees of the vertices of D. Moreover, the digraphs where this bound is attained are special classes of normally regular digraphs studied by Jørgensen in 2015 [6]. Finally, we construct normally regular digraphs where the equality is attained.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 552, 1 September 2018, Pages 194-209
Journal: Linear Algebra and its Applications - Volume 552, 1 September 2018, Pages 194-209
نویسندگان
Natalia Agudelo, Juan Rada, Mauricio Rivera,