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arXiv · 1612.02642

Center, centroid and subtree core of trees

Dheer Noal Sunil Desai·Kamal Lochan Patra
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Abstract

For $n\geq 5$ and $2\leq g\leq n-3,$ consider the tree $P_{n-g,g}$ on $n$ vertices which is obtained by adding $g$ pendant vertices to one degree $1$ vertex of the path $P_{n-g}$. We call the trees $P_{n-g,g}$ as path-star trees. We prove that over all trees on $n\geq 5$ vertices, the distance between center and subtree core and the distance between centroid and subtree core are maximized by some path-star trees. We also prove that the tree $P_{n-g_0,g_0}$ maximizes both the distances among all path-star trees on $n$ vertices, where $g_0$ is the smallest positive integer such that $2^{g_0}+g_0>n-1.$

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Dheer Noal Sunil Desai, Kamal Lochan Patra. 2016-12-08. Center, centroid and subtree core of trees. https://arxiv.org/abs/1612.02642

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