Relationships between rupture degree and other parameters
Zhiping Wang, Zhiping Wang, Zhongtuo Wang, Zhongtuo Wang · International Journal of Computer Mathematics · 2006
The rupture degree of an incomplete connected graph G is defined by where ω (G−X) denotes the number of components in the graph G−X and m(G−X) is the order of the largest component of G−X. For a complete graph K n , we define r(K n )=1−n. This parameter can be used to measure the vulnerability of a graph. To some extent, it represents a trade-off between the amount of work done to damage the network and how badly the network is damaged. In this paper, the relationships between the rupture degree and some other vulnerability parameters, namely the scattering number, toughness, integrity, and tenacity, are established. Examples show that the results are the best possible.