1-planar graph

Adjacency list

Combinatorics

Discrete mathematics

Graph

Mathematical analysis

Graph power

Chordal graph

Generalization

Adjacency matrix

Clique-sum

Line graph

Signed graph

Mathematics

Pathwidth

Two-graph

Indifference graph

The Art of Discrete and Applied Mathematics

Signed graphs are graphs whose edges get a sign +1 or −1 (the signature). Signed graphs can be studied by means of graph matrices extended to signed graphs in a natural way. Recently, the spectra of signed graphs have attracted much attention from graph spectra specialists. One motivation is that the spectral theory of signed graphs elegantly generalizes the spectral theories of unsigned graphs. On the other hand, unsigned graphs do not disappear completely, since their role can be taken by the special case of balanced signed graphs. Therefore, spectral problems defined and studied for unsigned graphs can be considered in terms of signed graphs, and sometimes such generalization shows nice properties which cannot be appreciated in terms of (unsigned) graphs. Here, we survey some general results on the adjacency spectra of signed graphs, and we consider some spectral problems which are inspired from the spectral theory of (unsigned) graphs.

Open problems in the spectral theory of signed graphs