An Algorithm to detect balancing of iterated line sigraph

A signed graph (or sigraph in short) S is a graph G in which each edge x carries a value [Formula: see text] called its sign denoted specially as [Formula: see text] . Given a sigraph S, H = L(S) called the line sigraph of S is that sigraph in which edges of S are represented as vertices, two of these vertices are defined to be adjacent whenever the corresponding edges in S have a vertex in common and any such edge ef is defined to be negative whenever both e and f are negative edges in S. Here S is called root sigraph of H. Iterated signed line graphs [Formula: see text] = [Formula: see text] k [Formula: see text] [Formula: see text] , S:= [Formula: see text] is defined similarly. In this paper, we give an algorithm to obtain iterated line sigraph and detect for which value of ‘k’ it is balanced and determine its complexity. In the end we will propose a technique that will use adjacency matrix of S and adjacency matrix of [Formula: see text] which is balanced for some ‘k’ as a parameter to encrypt a network and forward the data in the form of balanced [Formula: see text] and will decrypt it by applying inverse matrix operations.