ON THE AVERAGE LOWER 2-DOMINATION NUMBER OF A GRAPH

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 stations or 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 containing v. 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 by γ2av(G) = 1 |V (G)| P v∈V (G) γ2v(G). In this paper, above mentioned new parameter is defined and examined, also the average lower 2-domination number of well known graph families are calculated. Then upper and lower bounds are determined and exact formulas are found for the average lower 2-domination number of any graph G.