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Maximizing distance between center, centroid and subtree core of trees

  • Dheer Noal Sunil Desai
  • Kamal Lochan PatraEmail author
Article
  • 17 Downloads

Abstract

For \(n\ge 5\) and \(2\le g\le n-3,\) consider the tree \(P_{n-g,g}\) on n vertices which is obtained by adding g pendant vertices to one end vertex of the path \(P_{n-g}\). We call the trees \(P_{n-g,g}\) 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 \(n\ge 5\) 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 \(P_{n-g_0,g_0}\) maximizes both the distances among all path-star trees on n vertices, where \(g_0\) is the smallest positive integer satisfying \(2^{g_0}+g_0>n-1\).

Keywords

Tree center centroid subtree core distance 

Mathematics Subject Classification

05C05 05C12 

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Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  • Dheer Noal Sunil Desai
    • 1
    • 2
  • Kamal Lochan Patra
    • 1
    • 2
    Email author
  1. 1.School of Mathematical SciencesNational Institute of Science Education and Research (NISER)OdishaIndia
  2. 2.Homi Bhabha National Institute (HBNI)MumbaiIndia

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