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Math. Comput. Appl. 2016, 21(3), 29; https://doi.org/10.3390/mca21030029

# The Average Lower 2-Domination Number of Wheels Related Graphs and an Algorithm

Department of Mathematics, Faculty of Science, Karabük University, Karabük 78050, Turkey
Received: 4 March 2016 / Revised: 22 June 2016 / Accepted: 11 July 2016 / Published: 18 July 2016

# Abstract

The problem of quantifying the vulnerability of graphs has received much attention nowadays, especially in the field of computer or communication networks. In a communication network, the 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 graph as modeling a network, the average lower 2-domination number of a graph is a measure of the graph vulnerability and it is defined by $γ 2 a v ( G ) = 1 | V ( G ) | ∑ v ∈ V ( G ) γ 2 v ( G )$ , where the lower 2-domination number, denoted by $γ 2 v ( G )$ , of the graph G relative to v is the minimum cardinality of 2-domination set in G that contains the vertex v. In this paper, the average lower 2-domination number of wheels and some related networks namely gear graph, friendship graph, helm graph and sun flower graph are calculated. Then, we offer an algorithm for computing the 2-domination number and the average lower 2-domination number of any graph G. View Full-Text
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MDPI and ACS Style

Turaci, T. The Average Lower 2-Domination Number of Wheels Related Graphs and an Algorithm. Math. Comput. Appl. 2016, 21, 29.

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