(untitled) (European Journal of Pure and Applied Mathematics, 2024)
An ordered pair Σ = (Σ^u,σ) is called the signed graph, where Σ^u = (V,E) is a underlying graph and σ is a signed mapping, called signature, from E to the sign set +, - brace. The splitting signed graph Γ(Σ) of a signed graph Σ is defined as, for every vertex u V(Σ), take a new vertex u’. Join u’ to all the vertices of Σ adjacent to u such that σ_Γ(u’v) = σ(u’v), u 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 Σ and the energy of the splitting signed graph Γ(Σ) is established.