A Note on the Paired-Domination Subdivision Number of Trees

Abstract

For a graph G with no isolated vertex, let γpr(G) and sdγpr(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 sdγpr(T)≤min{γpr(T)2+1,n2}, improving the (n−1)-upper bound that was recently proven.

Keywords

• paired-domination number
• paired-domination subdivision number