Weakly status injective trees are status unique in trees

Jen Ling Shang, Tay Woei Shyu, Chiang Lin

Research output: Contribution to journalArticle

Abstract

The status of a vertex x in a graph is the sum of the distances between x and all other vertices. The status sequence of a graph is the list of the statuses of all vertices arranged in nondecreasing order. It is well known that non-isomorphic trees may have the same status sequence. We show that a tree is uniquely determined by its status sequence if the only pairs of vertices that have the same status are endvertices.

Original languageEnglish
Pages (from-to)133-143
Number of pages11
JournalArs Combinatoria
Volume139
Publication statusPublished - 2018 Jul
Externally publishedYes

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Keywords

  • Status
  • Status injective graph
  • Status sequence
  • Status unique graph
  • Tree
  • Weakly status injective tree

ASJC Scopus subject areas

  • Mathematics(all)

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