Perturbations in a signed graph and its index
Discussiones Mathematicae Graph Theory
Received 30.05.2016, Revised 23.02.2017, Accepted 23.02.2017, doi: 10.7151/dmgt.2035
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.
signed graph, switching equivalence, index, computer search