Graph Theory With Applications
Graph Theory With Applications
| Hi-index | 0.00 |
For the complete graph Kn, its rupture degree is defined as 1-n; and for a noncomplete connected graph G, its rupture degree is defined by r(G)=max{ω(G-X)-|X|-m(G-X):X ⊂ V(G), ω(G-X) 1 }, where ω(G-X) is the number of components of G-X and m(G-X) is the order of a largest component of G-X. It is shown that this parameter can be well used to measure the vulnerability of networks. Li and Li proved in 2004 that computing the rupture degree for a general graph is NP-complete. In this paper, we give a recursive algorithm for computing the rupture degree of trees, and determine the maximum and minimum rupture degree of trees with given order and maximum degree.