We introduce a new graph parameter, the rupture degree. The rupture degree for a complete graph Kn is defined as 1 − n, and the rupture degree for an incomplete connected graph G 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 paramete...

Reliability of networks is an important issue in the field of graph and network. Computation of network vulnerability parameters is NP-complete for popular network topologies such as tree, Mesh, Cube, etc.In this paper, we will show that the tenacity and rupture degree parameters for trapezoid graphs can be computed in polynomial time.

In general, computation of graph vulnerability parameters is NP-complete. In past, some algorithms were introduced to prove that computation of toughness, scattering number, integrity and weighted integrity parameters of interval graphs are polynomial. In this paper, two different vulnerability parameters of graphs, tenacity and rupture degree are defined. In general, computing the tenacity o...

Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructed when they do get disrupted. These desirable properties of networks can be measured by various parameters such as connectivity, toughness, tenacity and rupture degree. Among these parameters, rupture degree is comparatively better parameter ...

The rupture degree of a noncomplete-connected graph G is defined by , where the number components and order largest component of. In this paper, we determine some Cartesian product graphs.