Extremal connectivity and vulnerability in graphs

Abstract

If a practical network is modelled as a graph in which the lines are perfect but the points may fail then a primary measure of vulnerability is the point connectivity of the graph and one possible secondary measure of vulnerability is the number of minimum point disconnecting sets. The graph should have the maximum possible point connectivity and the minimum number of point disconnecting sets. A lower bound for the number of minimum point disconnecting sets is derived by identifying points with identical adjacencies.

Role of Graphic Integer Sequence in the Determination of Graph Integrity

“…This section contains some related works. First, in [20,21] authors used connectivity as the measure of vulnerability. Next, in [22] authors discussed the relationship between the safe number and integrity of a graph and in [23] authors studied the bounds and relationships among the scattering number, integrity, and tenacity which are better than other parameters for measuring the stability of networks.…”

Adaptive Network Layer

“…[97][98][99][100][101][102][103][104][105][106][107][108][109] are concerned with a number of other graph invariants that have an obvious connection with the notions of vulnerability and survivability of communications networks. [97][98][99][100][101][102][103][104][105][106][107][108][109] are concerned with a number of other graph invariants that have an obvious connection with the notions of vulnerability and survivability of communications networks.…”

Adaptive Network Layer

“…A number of references [99][100][101][102][103][104][105][106][107][108][109][110][111] are concerned with a number of other graph invariants that have an obvious connection with the notions of vulnerability and survivability of communications networks. The main concepts here are those of dominance, independence and covering of a graph with respect to either a set of nodes or a set of edges of the underlying graph.…”