The average lower reinforcement number of a graph

Creative Commons License

Turaci T., ASLAN E.

RAIRO - Theoretical Informatics and Applications, cilt.2014, ss.135-144, 2016 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2014
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1051/ita/2016015
  • Dergi Adı: RAIRO - Theoretical Informatics and Applications
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.135-144
  • Anahtar Kelimeler: Average lower reinforcement number, Connectivity, Domination number, Graph vulnerability, Network design and communication, Reinforcement number
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

Let G = (V(G),E(G)) be a simple undirected graph. The reinforcement number of a graph is a vulnerability parameter of a graph. We have investigated a refinement that involves the average lower reinforcement number of this parameter. The lower reinforcement number, denoted by re∗(G), is the minimum cardinality of reinforcement set in G that contains the edge e∗ of the complement graph G. The average lower reinforcement number of G is defined by rav (G)=1/E(G) ∑e∗∈E(G) re∗(G). In this paper, we define the average lower reinforcement number of a graph and we present the exact values for some well-known graph families.