Authors: Simić, Slobodan 
Stanić, Zoran
Title: Polynomial reconstruction of signed graphs
Journal: Linear Algebra and Its Applications
Volume: 501
First page: 390
Last page: 408
Issue Date: 15-Jul-2016
Rank: M21
ISSN: 0024-3795
DOI: 10.1016/j.laa.2016.03.036
The reconstruction problem of the characteristic polynomial of graphs from their polynomial decks was posed in 1973. So far this problem is not resolved except for some particular cases. Moreover, no counterexample for graphs of order n>2 is known. Here we put forward the analogous problem for signed graphs, and besides some general results, we resolve it within signed trees and unicyclic signed graphs, and also within disconnected signed graphs whose one component is either a signed tree or is unicyclic. A family of counterexamples that was encountered in this paper consists of two signed cycles of the same order, one balanced and the other unbalanced.
Keywords: Characteristic polynomial | Eigenvalues | Signed graph | Unicyclic graph
Publisher: Elsevier
Project: Graph theory and mathematical programming with applications in chemistry and computer science 
Geometry, Education and Visualization With Applications 

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