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- Title
Maximizing distance between center, centroid and subtree core of trees.
- Authors
Desai, Dheer Noal Sunil; Patra, Kamal Lochan
- Abstract
For n≥5 and 2≤g≤n-3, consider the tree Pn-g,g on n vertices which is obtained by adding g pendant vertices to one end vertex of the path Pn-g. We call the trees Pn-g,g as path-star trees. The subtree core of a tree T is the set of all vertices v of T for which the number of subtrees of T containing v is maximum. We prove that over all trees on n≥5 vertices, the distance between the center (respectively, centroid) and the subtree core is maximized by some path-star trees. We also prove that the tree Pn-g0,g0 maximizes both the distances among all path-star trees on n vertices, where g0 is the smallest positive integer satisfying 2g0+g0>n-1.
- Subjects
CENTROID; SET theory; GEOMETRIC vertices; CENTER (Mathematics); MATHEMATICS theorems
- Publication
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2019, Vol 129, Issue 1, p1
- ISSN
0253-4142
- Publication type
Article
- DOI
10.1007/s12044-018-0452-x