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- W3026975688 abstract "Let T be a tree with n vertices, and Dn be the distance matrix of T. Graham and Pollak (1971) discovered an elegant formula for the determinant of Dn: det(Dn)=−(n−1)(−2)n−2. It is surprising that it depends only on the order of T, not on the specific structure of T. By virtue of the classical Dodgson’s determinant-evaluation rule, Yan and Yeh (2006) presented a simple proof of the formula above. In this note, we give another simple proof, based on a homogeneous linear three-term recurrence relation: det(Dn)+4det(Dn−1)+4det(Dn−2)=0." @default.
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- W3026975688 date "2020-10-01" @default.
- W3026975688 modified "2023-09-25" @default.
- W3026975688 title "Another simple proof of Graham and Pollak’s theorem" @default.
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- W3026975688 doi "https://doi.org/10.1016/j.disc.2020.111994" @default.
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