Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 3 2026 09 01 A construction of cospectral signed line graphs 985 993 14877 10.22049/cco.2024.30034.2284 EN Zoran Stanić Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11 000 Belgrade, Serbia Journal Article 2024 09 30 For an ordinary graph $G$, we compute the eigenvalues and the eigenspaces of the signed line graph $\mathcal{L}(\ddot{G})$, where $\ddot{G}$ is obtained from $G$ by inserting a negative parallel edge between every pair of adjacent vertices. As an application, we prove that if $G$ and $H$ share the same vertex degrees, then $\mathcal{L}(\ddot{G})$ and $\mathcal{L}(\ddot{H})$ share the same spectrum. To the best of our knowledge, this construction does not follow the line of any known construction developed for either graphs or signed graphs. Among the other consequences, we emphasize that $\mathcal{L}(\ddot{G})$ is integral (i.e., its spectrum consists entirely of integers), which means that a construction of integral signed graphs has been established simultaneously. https://comb-opt.azaruniv.ac.ir/article_14877_f7086ec79f356f1b2522fdc3733cdc57.pdf