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.
On the largest eigenvalue of signed unicyclic graphs / Akbari, S.; Belardo, F.; Heydari, F.; Maghasedi, M.; Souri, M.. - In: LINEAR ALGEBRA AND ITS APPLICATIONS. - ISSN 0024-3795. - 581:(2019), pp. 145-162. [10.1016/j.laa.2019.06.016]
On the largest eigenvalue of signed unicyclic graphs
Belardo F.;
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.| File | Dimensione | Formato | |
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On the largest eigenvalue of signed unicyclic graphs.pdf
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