Exponential Domination Critical and Stability in Some Graphs


AYTAÇ A. , Atakul B. A.

INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE, cilt.30, ss.781-791, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 30 Konu: 5
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1142/s0129054119500217
  • Dergi Adı: INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE
  • Sayfa Sayıları: ss.781-791

Özet

An 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.