کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4603380 | 1336958 | 2008 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
An upper bound for the minimum rank of a graph
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
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چکیده انگلیسی
For a graph G of order n, the minimum rank of G is defined to be the smallest possible rank over all real symmetric n×n matrices A whose (i,j)th entry (for i≠j) is nonzero whenever {i,j} is an edge in G and is zero otherwise. We prove an upper bound for minimum rank in terms of minimum degree of a vertex is valid for many graphs, including all bipartite graphs, and conjecture this bound is true over for all graphs, and prove a related bound for all zero-nonzero patterns of (not necessarily symmetric) matrices. Most of the results are valid for matrices over any infinite field, but need not be true for matrices over finite fields.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 429, Issue 7, 1 October 2008, Pages 1629-1638
Journal: Linear Algebra and its Applications - Volume 429, Issue 7, 1 October 2008, Pages 1629-1638