Article ID Journal Published Year Pages File Type
4949799 Discrete Applied Mathematics 2017 10 Pages PDF
Abstract

Let Gσ=(V,E,σ) be a connected signed graph. Using the equivalence between signed graphs and 2-lifts of graphs, we show that the frustration index of Gσ is bounded from below and above by expressions involving another graph invariant, the smallest eigenvalue of the (signed) Laplacian of Gσ. From the proof, stricter bounds are derived. Additionally, we show that the frustration index is the solution to a l1-norm optimization problem over the 2-lift of the signed graph. This leads to a practical implementation to compute the frustration index. Also, leveraging the 2-lifts representation of signed graphs, a straightforward proof of Harary's theorem on balanced graphs is derived. Finally, real world examples are considered.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
Authors
,