کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4599576 1631141 2014 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Graphs that allow all the eigenvalue multiplicities to be even
ترجمه فارسی عنوان
نمودارهایی که اجازه می دهد همه مقادیر عدد خاص حتی یکسان باشند
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

Let G be an undirected graph on n   vertices and let S(G)S(G) be the set of all n×nn×n real symmetric matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. The Inverse Eigenvalue Problem for a graph G   is a problem of determining all possible lists that can occur as the lists of eigenvalues of matrices in S(G)S(G). This question is, in general, hard to answer and several variations were studied, most notably the minimum rank problem. In this paper we introduce the problem of determining for which graphs G   there exists a matrix in S(G)S(G) whose characteristic polynomial is a square, i.e. the multiplicities of all its eigenvalues are even. We solve this question for several families of graphs.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 454, 1 August 2014, Pages 72–90
نویسندگان
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