ON THE AVERAGE LOWER 2-DOMINATION NUMBER OF A GRAPH

Abstract

Computer scientists and network scientists want a speedy, reliable, and nonstop communication. In a communication network, the vulnerability measures the resistance of the network to disruption of operation after the failure of certain stationsor communication links. The average lower 2-domination number of a graph G relative to a vertex v is the cardinality of a minimum 2-dominating set in G containingv. Consider the graph G modeling a network. The average lower 2-domination number of G, denoted as γ2av G , is a new measure of the network vulnerability, given byγ2av G =defined and examined, also the average lower 2-domination number of well known graphfamilies are calculated. Then upper and lower bounds are determined and exact formulasare found for the average lower 2-domination number of any graph G