The average scattering number of graphs

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ASLAN E., Kilinç D., YÜCALAR F., BORANDAĞ E.

RAIRO - Theoretical Informatics and Applications, cilt.50, sa.3, ss.263-272, 2016 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 50 Sayı: 3
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1051/ita/2016027
  • Dergi Adı: RAIRO - Theoretical Informatics and Applications
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.263-272
  • Anahtar Kelimeler: Average lower domination number, Average lower independence number, Connectivity, Rupture degree, Scattering number
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

The scattering number of a graph is a measure of the vulnerability of a graph. In this paper we investigate a refinement that involves the average of a local version of the parameter. If v is a vertex in a connected graph G, then scv(G) = max {ω(G - Sv) - | Sv |}, where the maximum is taken over all disconnecting sets Sv of G that contain v. The average scattering number of G denoted by scav(G), is defined as scav(G) = Σv ϵ V(G) scv(G) / n, where n will denote the number of vertices in graph G. Like the scattering number itself, this is a measure of the vulnerability of a graph, but it is more sensitive. Next, the relations between average scattering number and other parameters are determined. The average scattering number of some graph classes are obtained. Moreover, some results about the average scattering number of graphs obtained by graph operations are given.