On the index of unbalanced signed bicyclic graphs

In this paper, we focus on the index (largest eigenvalue) of the adjacency matrix of connected signed graphs. We give some general results on the index when the corresponding signed graph is perturbed. As applications, we determine the first five largest indices among all unbalanced signed bicyclic graphs on n≥36\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 36$$\end{document} vertices together with the correspondingPlease provide MSC codes. For more details, if required, kindly visit http://www.ams.org/msc/. extremal signed graphs whose indices attain these values.