Computation of the eigenvalues of complete signed graphs

Shariefuddin Pirzada, Mir Riyaz Ul Rashid, Amir Rehman, Edy Tri Baskoro

Abstract


A signed graph Σ is the ordered pair (G,σ), where G=(V,E) is a finite simple graph, called the underlying graph, and σ: E(G) → {+1, -1} is a sign function or a signature of Σ. Let (K_n,σ) be a complete signed graph with n vertices. In this paper, we give a complete description of the adjacency, Laplacian and net Laplacian spectrum of a complete signed graph (K_n,σ) whenever its negative edges induce either a complete tripartite graph or a friendship graph. This is an addition to the class of complete signed graphs whose spectra is completely known.

Keywords


complete signed graph; complete tripartite graph; friendship graph; spectrum; Laplacian spectrum; net Laplacian spectrum

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DOI: http://dx.doi.org/10.5614/ejgta.2026.14.1.16

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