Computation of the eigenvalues of complete signed graphs - Pirzada, Shariefuddin; Ul Rashid, Mir Riyaz; Rehman, Amir; Baskoro, Edy Tri (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2026)
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.