The average lower reinforcement number of a graph
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 50 (2016) no. 2, pp. 135-144.

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. 𝑙𝑜𝑤𝑒𝑟 𝑟𝑒𝑖𝑛𝑓𝑜𝑟𝑐𝑒𝑚𝑒𝑛𝑡 𝑛𝑢𝑚𝑏𝑒𝑟 , denoted by r e * (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 r a v ( G ) = 1 | E ( G ¯ ) | Σ e * E ( G ¯ ) r e * ( 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.

DOI : 10.1051/ita/2016015
Classification : 05C40, 05C69, 68M10, 68R10
Mots-clés : Graph vulnerability, connectivity, network design and communication, domination number, reinforcement number, average lower reinforcement number
Turaci, Tufan 1 ; Aslan, Ersin 2

1 Department of Mathematics, Faculty of Science, Karabük University, 78050, Karabük, Turkey.
2 Turgutlu Vocational Training School, Celal Bayar University, 45400 Manisa, Turkey.
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Turaci, Tufan; Aslan, Ersin. The average lower reinforcement number of a graph. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 50 (2016) no. 2, pp. 135-144. doi : 10.1051/ita/2016015. http://archive.numdam.org/articles/10.1051/ita/2016015/

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