Integral trees with given nullity

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• 作者：E. Ghorbani^a ; ^b ; ^{e_ghorbani@ipm.ir" class="auth_mail" title="E-mail the corresponding author} ; A. Mohammadian^b ; ^{ali_m@ipm.ir" class="auth_mail" title="E-mail the corresponding author} ; B. Tayfeh-Rezaie^b ; ^{tayfeh-r@ipm.ir" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Adjacency eigenvalue ; Eigenvalue multiplicity ; Nullity ; Integral tree
• 刊名：Discrete Mathematics
• 出版年：2016
• 出版时间：6 January 2016
• 年：2016
• 卷：339
• 期：1
• 页码：157-164
• 全文大小：531 K

文摘

A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. We prove that for a given nullity more than 1, there are only finitely many integral trees. Integral trees with nullity at most 1 were already characterized by Watanabe and Brouwer. It is shown that integral trees with nullity 2 and 3 are unique.