Regular integrity in graphs

Abstract

The integrity is a vulnerability parameter which measures the strength of any communication network. In any chemical reaction, reactants are converted products. Burning fuels, smelting iron, making glass and pottery, brewing beer are the examples of activities incorporating chemical reactions. In this paper, we introduce a new vulnerability parameter known as the regular integrity which is defined as I r (G) = min S⊆V (G) {|S| + m r (G − S)}. After the removal of S,G − S contains regular components with same regularity and m r (G − S) denotes the regularity of G − S. This measure is useful to analyze the stability of a chemical structure after the removal of one or more atoms into the disjoint regular components. The study of this parameter is initiated and find the bigger chemical structures with the given number of atoms and regular integrity number. Also, a method for constructing this type of structures is presented.