On the distance spectra of graphs

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• 作者：Ghodratollah Aalipour^a ; ^b ; ^{alipour.ghodratollah@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Aida Abiad^c ; ^{aidaabiad@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Zhanar Berikkyzy^d ; ^{zhanarb@iastate.edu" class="auth_mail" title="E-mail the corresponding author} ; Jay Cummings^e ; ^{jjcummings@math.ucsd.edu" class="auth_mail" title="E-mail the corresponding author} ; Jessica De Silva^f ; ^{jessica.desilva@huskers.unl.edu" class="auth_mail" title="E-mail the corresponding author} ; Wei Gao^g ; ^{wgao2@gsu.edu" class="auth_mail" title="E-mail the corresponding author} ; Kristin Heysse^d ; ^{keheysse@iastate.edu" class="auth_mail" title="E-mail the corresponding author} ; Leslie Hogben^d ; ^h ; ^{lhogben@iastate.edu" class="auth_mail" title="E-mail the corresponding author} ; ^{hogben@aimath.org" class="auth_mail" title="E-mail the corresponding author} ; Franklin H.J. Kenterⁱ ; ^{franklin.h.kenter@rice.edu" class="auth_mail" title="E-mail the corresponding author} ; Jephian C.-H. Lin^d ; ^{chlin@iastate.edu" class="auth_mail" title="E-mail the corresponding author} ; Michael Tait^e ; ^{mtait@math.ucsd.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：05C12 ; 05C31 ; 05C50 ; 15A15 ; 15A18 ; 15B48 ; 15B57
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：497
• 期：Complete
• 页码：66-87
• 全文大小：474 K

文摘

The distance matrix of a graph G is the matrix containing the pairwise distances between vertices. The distance eigenvalues of G are the eigenvalues of its distance matrix and they form the distance spectrum of G. We determine the distance spectra of double odd graphs and Doob graphs, completing the determination of distance spectra of distance regular graphs having exactly one positive distance eigenvalue. We characterize strongly regular graphs having more positive than negative distance eigenvalues. We give examples of graphs with few distinct distance eigenvalues but lacking regularity properties. We also determine the determinant and inertia of the distance matrices of lollipop and barbell graphs.