The Neighbor Toughness of Wheels and Related Networks
Abstract
In a network (communication, computer, transportation), the vulnerability parameters measure the resistance of the network to disruption of operation after the failure of certain stations or communication links. The neighbor toughness of a graph G is defined as ( ) ( / ) NT G min : ( / ) G S S G S $ 1 ~ = ( ~ 2, where S is any vertex subversion strategy of G and ω(G/S) is the number of connected components in the graph G/S. In this paper, the relations between neighbor toughness and other parameters are determined. Next, the neighbor toughness of wheels and some related networks namely gear, helm, sunflower and friendshipgraph are calculated.