Center, centroid and subtree core of trees

  title={Center, centroid and subtree core of trees},
  author={Dheer Noal Sunil Desai and Kamal Lochan Patra},
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… CONTINUE READING

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