Proof of a conjecture of Graham and Lov\'asz concerning unimodality of coefficients of the distance characteristic polynomial of a tree

DOI10.13001/1081-3810,1537-9582.3493zbMath1396.05062arXiv1507.02341MaRDI QIDQ4685888

Jephian C.-H. Lin, Franklin H. J. Kenter, Aida Abiad, Michael Tait, Ghodratollah Aalipour, Zhanar Berikkyzy, Leslie Hogben

Publication date: 9 October 2018

Full work available at URL: https://arxiv.org/abs/1507.02341

zbMATH Keywords

characteristic polynomialunimodaldistance matrixlog-concave

Mathematics Subject Classification ID

Graph polynomials (05C31) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Distance in graphs (05C12)

Related Items (1)

Graphs that are cospectral for the distance Laplacian

Uses Software

• SageMath

Cites Work

• Unnamed Item
• On the distance matrix of a tree
• Distance matrix polynomials of trees
• Distance spectra of graphs: a survey
• On a conjecture of Graham and Lovász about distance matrices
• Unimodality, log-concavity, real-rootedness and beyond
• Unimodality problems in Ehrhart theory
• On the Addressing Problem for Loop Switching

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