The problem of quantifying the vulnerability of graphs has received much attention\nnowadays, especially in the field of computer or communication networks. In a communication\nnetwork, the vulnerability measures the resistance of the network to disruption of operation after\nthe failure of certain stations or communication links. If we think of a graph as modeling a network,\nthe average lower 2-domination number of a graph is a measure of the graph vulnerability and\nit is defined by Ã?³2avpGq ââ?¬Å? 1\n|VpGq|\nÃ?â?¢\nvPVpGq Ã?³2vpGq, where the lower 2-domination number, denoted\nby Ã?³2vpGq, of the graph G relative to v is the minimum cardinality of 2-domination set in G that\ncontains the vertex v. In this paper, the average lower 2-domination number of wheels and some\nrelated networks namely gear graph, friendship graph, helm graph and sun flower graph are\ncalculated. Then, we offer an algorithm for computing the 2-domination number and the average\nlower 2-domination number of any graph G.
Loading....