Inequalities for Laplacian Eigenvalues of Signed Graphs with Given Frustration Number

Milica Anđelić, Tamara Koledin, Zoran Stanić
2021 Symmetry  
Balanced signed graphs appear in the context of social groups with symmetric relations between individuals where a positive edge represents friendship and a negative edge represents enmities between the individuals. The frustration number f of a signed graph is the size of the minimal set F of vertices whose removal results in a balanced signed graph; hence, a connected signed graph G˙ is balanced if and only if f=0. In this paper, we consider the balance of G˙ via the relationships between the
more » ... frustration number and eigenvalues of the symmetric Laplacian matrix associated with G˙. It is known that a signed graph is balanced if and only if its least Laplacian eigenvalue μn is zero. We consider the inequalities that involve certain Laplacian eigenvalues, the frustration number f and some related invariants such as the cut size of F and its average vertex degree. In particular, we consider the interplay between μn and f.
doi:10.3390/sym13101902 fatcat:xh35iommbzhcnjmf3kaphssn2q