Spectral analysis of <i>t</i>-path signed graphs

Sinha, Deepa; Rao, Anita Kumari; Dhama, Ayushi

doi:10.1080/03081087.2018.1472737

Cited by 4 publications

(2 citation statements)

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“…In recent years, researchers have explored the spectral properties of graphs constructed through graph operations such as disjoint union, Cartesian product, Kronecker product, strong product, lexicographic product, corona, edge corona, and neighbourhood corona. A comprehensive overview of results on the spectra of these graphs can be found in the literature [ [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] ] and one can find the properties of derived signed graphs in [ [13] , [14] , [15] , [16] , [17] , [18] ]. In [ 19 ] authors presented the idea of the splitting graph

for a given graph

.…”

Section: Introductionmentioning

confidence: 99%

An algorithmic characterization and spectral analysis of canonical splitting signed graph ξ(Σ)

Sinha,

Kumar

2024

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for a given graph

.…”

Section: Introductionmentioning

confidence: 99%

An algorithmic characterization and spectral analysis of canonical splitting signed graph ξ(Σ)

Sinha,

Kumar

2024

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“…The study of graph energy can provide insights into the structural properties of the graph and is often used in the design and analysis of communication networks, molecular chemistry, and social networks. Additionally, the energy of a graph is closely related to its spectrum and can be used to investigate various graph invariants, such as chromatic number, clique number, and independence number [5,7,8,12,16]. Sinha et.al [13] introduced the splitting signed graphs as an extension of the splitting graph concept.…”

Section: Introductionmentioning

confidence: 99%

Spectral Analysis of Splitting Signed Graph

Kumar,

Sinha

2024

Eur. J. Pure Appl. Math.

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An ordered pair $\Sigma = (\Sigma^{u}$,$\sigma$) is called the \textit{signed graph}, where $\Sigma^{u} = (V,E)$ is a \textit{underlying graph} and $\sigma$ is a signed mapping, called \textit{signature}, from $E$ to the sign set $\lbrace +, - \rbrace$. The \textit{splitting signed graph} $\Gamma(\Sigma)$ of a signed graph $\Sigma$ is defined as, for every vertex $u \in V(\Sigma)$, take a new vertex $u'$. Join $u'$ to all the vertices of $\Sigma$ adjacent to $u$ such that $\sigma_{\Gamma}(u'v) = \sigma(u'v), \ u \in N(v)$. The objective of this paper is to propose an algorithm for the generation of a splitting signed graph, a splitting root signed graph from a given signed graph using Matlab. Additionally, we conduct a spectral analysis of the resulting graph. Spectral analysis is performed on the adjacency and laplacian matrices of the splitting signed graph to study its eigenvalues and eigenvectors. A relationship between the energy of the original signed graph $\Sigma$ and the energy of the splitting signed graph $\Gamma(\Sigma)$ is established.

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