Switching invariant two-path signed graphs

Gill, M.K; Patwardhan, G.A

doi:10.1016/0012-365x(86)90090-7

Cited by 5 publications

(4 citation statements)

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“…By property P :� P(v i , v j ), we mean that if property P(v i , v j ; v) holds for one common neighbor v of v i and v j , then it holds for every common neighbor v of v i and v j . e 2-path signed network [34] (Σ) 2 � (V, E ′ , σ ′ ) of a signed network Σ � (V, E, σ) is defined as follows. e vertex set is the same as the original signed network Σ, and two vertices u, v ∈ V((Σ) 2 ) are adjacent if and only if there exist a path of length two in Σ. e edge uv ∈ V((Σ) 2 ) is negative if and only if all the edges in all the two paths in Σ between them are negative otherwise the edge is positive.…”

Section: Definitions and Preliminariesmentioning

confidence: 99%

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Characterization of 2-Path Signed Network

Sinha

Sharma

2020

Complexity

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A signed network is a network where each edge receives a sign: positive or negative. In this paper, we report our investigation on 2-path signed network of a given signed network Σ , which is defined as the signed network whose vertex set is that of Σ and two vertices in Σ 2 are adjacent if there exist a path of length two between them in Σ . An edge ab in Σ 2 receives a negative sign if all the paths of length two between them are negative, otherwise it receives a positive sign. A signed network is said to be if clusterable its vertex set can be partitioned into pairwise disjoint subsets, called clusters, such that every negative edge joins vertices in different clusters and every positive edge joins vertices in the same clusters. A signed network is balanced if it is clusterable with exactly two clusters. A signed network is sign-regular if the number of positive (negative) edges incident to each vertex is the same for all the vertices. We characterize the 2-path signed graphs as balanced, clusterable, and sign-regular along with their respective algorithms. The 2-path network along with these characterizations is used to develop a theoretic model for the study and control of interference of frequency in wireless communication networks.

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Section: Definitions and Preliminariesmentioning

confidence: 99%

“…Signed networks of some intersection networks have been already studied [30][31][32][33]. Also path graphs of signed graphs are discussed in [34][35][36][37][38]. In this paper, we try and establish the results for signed networks defined on 2-path networks.…”

Section: Introductionmentioning

confidence: 99%

Characterization of 2-Path Signed Network

Sinha

Sharma

2020

Complexity

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“…The idea of switching a signed graph was introduced by Abelson and Rosenberg [ 36 ] in connection with structural analysis of social behaviour and may be formally stated as follows: given a marking μ of a signed graph S , switching S with respect to μ is the operation of changing the sign of every edge of S to its opposite whenever its end vertices are of opposite signs in S μ ( also see Gill and Patwardhan [ 37 , 38 ]). The signed graph obtained in this way is denoted by ( S ) μ and is called the μ - switched signed graph or just switched signed graph when the marking is clear from the context.…”

Section: Introductionmentioning

confidence: 99%

Characterization of 2-Path Product Signed Graphs with Its Properties

Sinha

Sharma

2017

Computational Intelligence and Neuroscience

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A signed graph is a simple graph where each edge receives a sign positive or negative. Such graphs are mainly used in social sciences where individuals represent vertices friendly relation between them as a positive edge and enmity as a negative edge. In signed graphs, we define these relationships (edges) as of friendship (“+” edge) or hostility (“−” edge). A 2-path product signed graph Strue#^S of a signed graph S is defined as follows: the vertex set is the same as S and two vertices are adjacent if and only if there exists a path of length two between them in S. The sign of an edge is the product of marks of vertices in S where the mark of vertex u in S is the product of signs of all edges incident to the vertex. In this paper, we give a characterization of 2-path product signed graphs. Also, some other properties such as sign-compatibility and canonically-sign-compatibility of 2-path product signed graphs are discussed along with isomorphism and switching equivalence of this signed graph with 2-path signed graph.

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“…[12] A signed graph Σ is balanced if and only if its vertex set V (Σ) can be partitioned into two subsets V 1 and V 2 (one of them possibly empty) such that every negative edge of Σ joins a vertex of V 1 with one of V 2 while no positive edge does so. Now by a positive section (negative section) [10] in a signed graph Σ , we mean a maximal edge induced weakly connected subsigned graph consisting of only positive (negative) edges of Σ that turn out to be simply a path (semipath) if Σ is a cycle (semicycle). For a signed graph Σ , Behzad and Chartrand [6] defined its line signed graph L(Σ) as the signed graph in which the edges of Σ are represented as vertices.…”

Section: (C) γ 2 (R) Is Totally Disconnected If and Only If R Is A Lomentioning

confidence: 99%

Co-maximal signed graphs of commutative rings

2018

Turk J Math

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Switching invariant two-path signed graphs

Cited by 5 publications

References 4 publications

Characterization of 2-Path Signed Network

Characterization of 2-Path Signed Network

Characterization of 2-Path Product Signed Graphs with Its Properties

Co-maximal signed graphs of commutative rings

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