Aytac, AysunAtakul, Betul Atay2019-10-272019-10-2720190129-05411793-63730129-05411793-6373https://doi.org/10.1142/S0129054119500217https://hdl.handle.net/11454/28728An exponential dominating set of graph G = (V, E) is a kind of distance domination subset S subset of V(G) such that Sigma(u is an element of S)(1/2)((d) over bar (u,v)-1) >= 1, for all v E V(G), where (d) over bar (u, v) is the length of a shortest path in < V(G)- (S - {u})> if such a path exists, and Do otherwise. The minimum exponential domination number, gamma(e) (G) is the smallest cardinality of an exponential dominating set. The minimum exponential domination number, gamma(e) (G) can be decreased or increased by removal of some vertices from G. In this paper, we investigate of this phenomenon which is referred to critical and stability in graphs.en10.1142/S0129054119500217info:eu-repo/semantics/openAccessGraph vulnerabilitynetwork design and communicationdominationexponential domination numberArticle305781791WOS:000481542900006Q3Q4