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On the largest eigenvalue of signed unicyclic graphs
, Article Linear Algebra and Its Applications ; Volume 581 , 2019 , Pages 145-162 ; 00243795 (ISSN) ; Belardo, F ; Heydari, F ; Maghasedi, M ; Souri, M ; Sharif University of Technology
Elsevier Inc
2019
Abstract
Signed graphs are graphs whose edges get signs ±1 and, as for unsigned graphs, they can be studied by means of graph matrices. Here we focus our attention to the largest eigenvalue, also known as the index of the adjacency matrix of signed graphs. Firstly we give some general results on the index variation when the corresponding signed graph is perturbed. Also, we determine signed graphs achieving the minimal or the maximal index in the class of unbalanced unicyclic graphs of order n≥3. © 2019