Signed graphs with two eigenvalues and vertex degree five - Stanić, Zoran (Ars mathematica contemporanea, 2022)
It is known that a signed graph with exactly 2 eigenvalues must be regular, and all those whose vertex degree does not exceed 4 are known. In this paper we characterize all signed graphs with 2 eigenvalues and vertex degree 5. We also determine all signed graphs with 2 eigenvalues and 12 or 13 vertices, which is a natural step since those with a fewer number of vertices are known.
Keywords: adjacency matrix; bipartite double; dvodelni dvojnik; matrika sosednosti; regular signed graph; regularen označeni graf; utežna matrika; weighing matrix