%0 Journal Article %T Signed bicyclic graphs with minimal index %J Communications in Combinatorics and Optimization %I Azarbaijan Shahid Madani University %Z 2538-2128 %A Brunetti, Maurizio %A Ciampella, Adriana %D 2023 %\ 03/01/2023 %V 8 %N 1 %P 207-241 %! Signed bicyclic graphs with minimal index %K Signed graph %K Bicyclic Graph %K Index %K Extremal Graph Theory %R 10.22049/cco.2022.27346.1241 %X The index $\lambda_1(\Gamma)$ of a signed graph $\Gamma=(G,\sigma)$ is just the largest eigenvalue of its adjacency matrix. For any $n \geqslant 4$ we identify the signed graphs achieving the minimum index in the class of signed bicyclic graphs with $n$ vertices. Apart from the $n=4$ case, such graphs are obtained by considering a starlike tree with four branches of suitable length (i.e.\ four distinct paths joined at their end vertex $u$) with two additional negative independent edges pairwise joining the four vertices adjacent to $u$. As a by-product, all signed bicyclic graphs containing  a theta-graph and whose index is less than $2$ are detected. %U http://comb-opt.azaruniv.ac.ir/article_14348_9f0156787274798785c37d2073e8e83d.pdf