On the Paired-Domination Subdivision Number of a Graph

In order to increase the paired-domination number of a graph G, the minimum number of edges that must be subdivided (where each edge in G can be subdivided no more than once) is called the paired-domination subdivision number sd γ p r ( G ) of G. It is well known that sd γ p r ( G + e ) can be smaller or larger than sd γ p r ( G ) for some edge e ∉ E ( G ) . In this note, we show that, if G is an isolated-free graph different from m K 2 , then, for every edge e ∉ E ( G ) , sd γ p r ( G + e ) ≤ sd γ p r ( G ) + 2 Δ ( G ) .