The maximum of the minimal multiplicity of eigenvalues of symmetric matrices whose pattern is constrained by a graph

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• 作者：Polona Oblak^a ; ^{polona.oblak@fri.uni-lj.si" class="auth_mail" title="E-mail the corresponding author} ; Helena &Scaron ; migoc^b ; ^{helena.smigoc@ucd.ie" class="auth_mail" title="E-mail the corresponding author}
• 关键词：05C50 ; 15A18 ; 15B57
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：512
• 期：Complete
• 页码：48-70
• 全文大小：425 K

文摘

In this paper we introduce a parameter si1" class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630413X&_mathId=si1.gif&_user=111111111&_pii=S002437951630413X&_rdoc=1&_issn=00243795&md5=b7e3358fddb55fe03659090b7a8583bb" title="Click to view the MathML source">Mm(G)class="mathContainer hidden">class="mathCode">, defined as the maximum over the minimal multiplicities of eigenvalues among all symmetric matrices corresponding to a graph G  . We develop basic properties of si1" class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630413X&_mathId=si1.gif&_user=111111111&_pii=S002437951630413X&_rdoc=1&_issn=00243795&md5=b7e3358fddb55fe03659090b7a8583bb" title="Click to view the MathML source">Mm(G)class="mathContainer hidden">class="mathCode"> and compute it for several families of graphs.