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
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
An upper bound for the minimum rank of a graph
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