On 2-path signed graphs

Sinha, Deepa; Sharma, Deepakshi

doi:10.1109/iwci.2016.7860369

Cited by 5 publications

(4 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this article balancedness and consistency of 2-path signed graph [31] of a balanced and consistent signed graph have been discussed for cycles, star graphs and trees. We have obtained necessary and sufficient condition under which 2-path signed graph of a balanced and consistent graph Σ is consistent and balanced when G is a cycle, star graph or tree.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

On balance and consistency preserving 2-path signed graphs

Chettri,

Deb,

Gautam

2023

EJGTA

View full text Add to dashboard Cite

Let Σ = (G, σ) be a balanced and canonically consistent signed graph. The 2-path signed graph Σ#Σ = (G 2 , σ ′ ) of Σ has the underlying graph as G 2 and the sign σ ′ (uv) of an edge uv in it is −1 whenever in each uv-path of length 2 in Σ all edges are negative; otherwise σ ′ (uv) is 1. Here, G 2 is the graph obtained from G by adding an edge between u and v if there is a path of length 2 between them. In this article, we have investigated balancedness and canonically consistency of 2-path signed graphs Σ#Σ of a balanced and canonically consistent signed graph Σ. The problem has been resolved completely for cycles, star graphs and trees.

show abstract

Section: Discussionmentioning

confidence: 99%

“…The 2-path signed graph is defined by Sinha [31] and discussed the conditions under which a signed graph would be a 2-path signed graph. In this article, we attempted to study the canonically consistent balanced signed graphs whose 2-path signed graphs is also canonically consistent and balanced.…”

Section: Introductionmentioning

confidence: 99%

On balance and consistency preserving 2-path signed graphs

Chettri,

Deb,

Gautam

2023

EJGTA

View full text Add to dashboard Cite

show abstract

“…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. e definition of 2-path signed network was used [53], to bring out some basic results, which was further extended and shaped in the present paper. e 2 subsets v i , v j having property P are named as P pairs and the set of all P pairs is denoted by P * .…”

Section: Definitions and Preliminariesmentioning

confidence: 99%

Characterization of 2-Path Signed Network

Sinha

Sharma

2020

Complexity

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…Assume that S = ( V , E , σ ) is a signed graph. We associate with S the 2-path signed graph [ 39 ] S # S = ( V , E ′, σ ′) defined as follows: the vertex set is same as the original signed graph S and two vertices u , v ∈ V ( S # S ), are adjacent if and only if there exists a path of length two in S . The edge uv ∈ V ( S # S ) is negative if and only if all the edges in all the two paths in S are negative otherwise the edge is positive (see Figure 1 ).…”

Section: Introductionmentioning

confidence: 99%

Characterization of 2-Path Product Signed Graphs with Its Properties

Sinha

Sharma

2017

Computational Intelligence and Neuroscience

Self Cite

View full text Add to dashboard Cite

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.

show abstract

On 2-path signed graphs

Cited by 5 publications

References 5 publications

On balance and consistency preserving 2-path signed graphs

On balance and consistency preserving 2-path signed graphs

Characterization of 2-Path Signed Network

Characterization of 2-Path Product Signed Graphs with Its Properties

Contact Info

Product

Resources

About