Rupture Degree and Middle Graphs

Abstract

Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructible if they do get disrupted. These desirable properties of networks can be measured by various parameters like connectivity, toughness, integrity, tenacity and scattering number. The rupture degree of a graph is a new parameter to measure the vulnerability of networks. For the complete graph K, rupture degree is defined as 1-n and for an incomplete connected graph G, rupture degree is defined by r(G) = max{w(G-S)-vertical bar S vertical bar-m(G-S) : S subset of V(G), w(G-S) > 1}, where w(G - S) is the number of components of G S and in m(G - S) is the order of a largest component of G - S. Rupture degree is independent from the other vulnerability parameters. In this paper, rupture degree of middle graphs is considered.