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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Ul Rashid, Mir Riyaz
University of Kashmir
Electrical & Electronics Engineering

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Computation of the eigenvalues of complete signed graphs Pirzada, Shariefuddin; Ul Rashid, Mir Riyaz; Rehman, Amir; Baskoro, Edy Tri
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 1 (2026): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2026.14.1.16

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.
Co-Authors Baskoro, Edy Tri Pirzada, Shariefuddin Rehman, Amir