An Optimal Algorithm to Detect Sign Compatibility of a Given Sigraph

Sinha, Deepa; Sethi, Anshu

doi:10.1007/s40009-014-0317-5

Cited by 5 publications

(3 citation statements)

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“…A sigraph S is sign-compatible [9] if there exists a marking μ of its vertices such that the end vertices of every negative edge receive "-" signs in μ and no positive edge in S has both of its ends assigned "-" sign in μ. In other words, a sigraph is sign-compatible if and only if its vertices can be partitioned into two subsets V 1 and V 2 such that the all-negative subsigraph of S is precisely the subsigraph induced by exactly one of the subsets V 1 and V 2 .…”

Section: Introductionmentioning

confidence: 99%

“…Based on concept sign-compatible sigraphs [9], characterization of line sigraphs [10] and algorithm to detect a line graph and output its root graph by Lehot [2], we will provide a computer-oriented characterization of line sigraph that will output the root sigraph S of sigraph H (sometimes called L(S)) whenever the latter is a line sigraph.…”

Section: Introductionmentioning

confidence: 99%

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Encryption using Network and Matrices through Signed Graphs

Sinha¹,

Sethi²

2016

IJCA

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Security of a network is important to all organizations, personal computer users, and the military. With the invention of the Internet, major concern is about the security and the history of security allows a better understanding of the emergence of security technology. One of the ways to secure businesses from the Internet is through firewalls and encryption mechanisms. A network can be designed as a sigraph S where every sigraph will have its unique adjacency matrix associated with it. A signed graph (or sigraph in short) S is a graph G in which every edge x carries a value s(x) ∈ {-1, +1} called its sign denoted specially as S = (G, s). 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 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. In this paper first we give an algorithm to obtain a line sigraph [1] and line root sigraph from a given sigraph [1], if it exists. This algorithm is an extension of an algorithm given by Lehot [2] in the realm of sigraphs. In the end we will propose a technique that will use adjacency matrix of S as a parameter to encrypt and forward the data in the form of adjacency matrix of L(S) and will decrypt it by applying inverse matrix operations.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Encryption using Network and Matrices through Signed Graphs

Sinha¹,

Sethi²

2016

IJCA

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“…A sigraph S is sign-compatible Sinha ( 2005 ); Sinha and Sethi 2015 ) if there exists a marking of its vertices such that the end vertices of every negative edge receive ‘−’ signs in and no positive edge in S has both of its ends assigned ‘−’ sign in In other words, a sigraph is sign-compatible if and only if its vertices can be partitioned into two subsets and such that the all-negative subsigraph of S is precisely the subsigraph induced by exactly one of the subsets and Every line sigraph is sign-compatible. However, not every sign-compatible sigraph need be line sigraph.…”

Section: Introductionmentioning

confidence: 99%

An Algorithm to detect balancing of iterated line sigraph

Sinha

Sethi

2015

SpringerPlus

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A signed graph (or sigraph in short) S is a graph G in which each edge x carries a value called its sign denoted specially as . 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 = k , S:= 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 which is balanced for some ‘k’ as a parameter to encrypt a network and forward the data in the form of balanced and will decrypt it by applying inverse matrix operations.

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Iterated local transitivity model for signed social networks

Sinha

Sharma

2017

AAECC

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An Optimal Algorithm to Detect Sign Compatibility of a Given Sigraph

Cited by 5 publications

References 1 publication

Encryption using Network and Matrices through Signed Graphs

Encryption using Network and Matrices through Signed Graphs

An Algorithm to detect balancing of iterated line sigraph

Iterated local transitivity model for signed social networks

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