Inverse domination integrity of graphs

Abstract

With the growing demand for information transport, networks and network architecture have grown increasingly vital. Nodes and the connections that connect them make up a communication network. When the communication network’s nodes or links are destroyed, the network’s efficiency reduces. If a network is modeled by a graph, then there are various graph theoretical parameters used to express the vulnerability of communication networks such as connectivity, integrity, weak integrity, neighbor integrity, hub integrity, domination integrity, toughness, tenacity etc. In this paper, we introduce a new vulnerability parameter known as an inverse domination integrity which is defined as IDI(G) = min S?V (G) {|S| + m(G ? S)}, where S is an inverse dominating set and m(G ? S) denotes the order of largest component of G ? S. We derive few bounds of an inverse domination integrity of graphs. Also, we determine an inverse domination integrity of some families of graphs. Finally, we compute different types of measures of vulnerabilities of probabilistic neural network which are useful in classification and pattern recognition problems.