4.7 Article

A Note on the Paired-Domination Subdivision Number of Trees

Journal

MATHEMATICS
Volume 9, Issue 2, Pages -

Publisher

MDPI
DOI: 10.3390/math9020181

Keywords

paired-domination number; paired-domination subdivision number

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Funding

  1. National Natural Science Foundation of China [61632002]
  2. National Key R&D Program of China [2018YFB1005100]

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In this note, it is shown that for a tree different from a healthy spider, the paired-domination subdivision number satisfies a certain condition, improving the existing upper bound.
For a graph G with no isolated vertex, let gamma(pr)(G) and sd(gamma pr)(G) denote the paired-domination and paired-domination subdivision numbers, respectively. In this note, we show that if T is a tree of order n >= 4 different from a healthy spider (subdivided star), then sd(gamma pr)(T) <= min{gamma(pr)(T)/2 + 1, n/2}, improving the (n-1)-upper bound that was recently proven.

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