Critical and stable pendant domination

Let S be a dominating set of a graph G . The set S is called a pendant dominating set of G if the induced subgraph of S contains a minimum of one node of degree one. The minimum cardinality of the pendant dominating set in G is referred to as the pendant domination number of G , indicated by γ p e ( G ) . This article analyzes the effect of γ p e ( G ) when an arbitrary node or edge is removed.