Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

THE AVERAGE LOWER 2-DOMINATION NUMBER OF WHEELS RELATED GRAPHS AND AN ALGORITHM

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Version 1 : Received: 14 July 2016 / Approved: 15 July 2016 / Online: 15 July 2016 (09:50:33 CEST)

A peer-reviewed article of this Preprint also exists.

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

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 γ2av(G)=1|V(G)|vV(G)γ2v(G), where the lower 2-domination number, denoted by γ2v(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.

Keywords

graph vulnerability; connectivity; network design and communication; domination number; average lower 2-domination number

Subject

Computer Science and Mathematics, Computer Vision and Graphics

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