|کد مقاله||کد نشریه||سال انتشار||مقاله انگلیسی||ترجمه فارسی||نسخه تمام متن|
|4949799||1364257||2017||10 صفحه PDF||سفارش دهید||دانلود کنید|
Let GÏ=(V,E,Ï) be a connected signed graph. Using the equivalence between signed graphs and 2-lifts of graphs, we show that the frustration index of GÏ is bounded from below and above by expressions involving another graph invariant, the smallest eigenvalue of the (signed) Laplacian of GÏ. 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.
Journal: Discrete Applied Mathematics - Volume 217, Part 2, 30 January 2017, Pages 276-285