An algorithm to detect s-consistency in line sigraph

By : Deepa Sinha , Anshu Sethi

Page No: 61-91

Abstract
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. For a given sigraph H, H is sigraph marked if the vertices of H are marked with the signs of the distinct edges of some sigraph M, called a marker of H, in a one-to-one manner such that adjacent vertices of H receive the signs of adjacent edges of M; (often, it is convenient to say that H is M-Marked when M is to be specified); H is then said to be S-Consistent whenever a marker S is to be specified, if there is an S-Marking ? of H with respect to which the marked sigraph H? is consistent. In this paper, we give an algorithm to obtain a line sigraph and detect whether it is S-Consistent or not and determine its complexity. In the end we will propose a technique that will use adjacency matrix of S and adjacency matrix of L(S) which is S-Consistent as a parameter to encrypt an image and forward the data in the form of S-Consistent L(S) and will decrypt it by applying inverse image and matrix operations.

Authors :
Deepa Sinha : South Asian University Akbar Bhawan, Chanakyapuri New Delhi- 110 021, India.
Anshu Sethi : Center For Mathematical Sciences Banasthali University Banasthali- 304 022 Rajasthan, India.