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- Title
A Conjecture on Different Central Parts of Binary Trees.
- Authors
Pandey, Dinesh; Patra, Kamal Lochan
- Abstract
Let Ω n be the family of binary trees on n vertices obtained by identifying the root of an rgood binary tree with a vertex of maximum eccentricity of a binary caterpillar. In the paper titled “On different middle parts of a tree" (The Electronic Journal of Combinatorics, 25 (2018), no. 3, paper 3.17, 32 pp), Smith et al. conjectured that among all binary trees on n vertices the pairwise distance between any two of center, centroid and subtree core is maximized by some member of the family Ω n . We first obtain the rooted binary tree which minimizes the number of root-containing subtrees and then prove this conjecture. We also obtain the binary trees which maximize these distances.
- Publication
Graphs & Combinatorics, 2022, Vol 38, Issue 6, p1
- ISSN
0911-0119
- Publication type
Article
- DOI
10.1007/s00373-022-02596-7