Geodesic
Perturbations in a Signed Graph and its Index
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 3, pp. 841-852

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In this paper we consider the behaviour of the largest eigenvalue (also called the index) of signed graphs under small perturbations like adding a vertex, adding an edge or changing the sign of an edge. We also give a partial ordering of signed cacti with common underlying graph by their indices and demonstrate a general method for obtaining lower and upper bounds for the index. Finally, we provide our computational results related to the generation of small signed graphs.
Keywords: signed graph, switching equivalence, index, computer search 
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Stanić, Zoran. Perturbations in a Signed Graph and its Index. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 3, pp. 841-852. http://geodesic.mathdoc.fr/item/DMGT_2018_38_3_a13/