On the rupture degree of a graph

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KIRLANGIÇ A., BACAK TURAN G.

Neural Network World, cilt.22, sa.1, ss.39-51, 2012 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 1
  • Basım Tarihi: 2012
  • Doi Numarası: 10.14311/nnw.2012.22.003
  • Dergi Adı: Neural Network World
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.39-51
  • Anahtar Kelimeler: Complete k-ary tree, Connectivity, Networks, Rupture degree, Vulnerability
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

In a communication network, vulnerability measures the resistance of the network to disruption of operation after the failure of certain stations or communication links. If we think of a connected graph as model-ing a network, the rupture degree of a graph is one measure of graph vulnerability and it is denned by r(G) = max(w(G - S) - |S| - m(G - S): S C V(G), w(G - S) > 1}, where w(G - S) is the number of components of G - S and m(G - S) is the order of a largest component of G - S. In this paper, general results on the rupture degree of a graph are considered. Firstly, some bounds on the rupture degree are given. Further, rupture degree of a complete k-ary tree is calculated. Also several results are given about complete k-ary tree and graph operations. Finally, we give formulas for the rupture degree of the cartesian product of some special graphs. © ICS AS CR 2012.