Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Articles in Press 2025 07 08 On Distance Induced Seidel Matrices for Signed Graphs 14983 10.22049/cco.2025.30248.2382 EN Biju K Department of Mathematics, P R N S S College, Mattannur, Kannur, Kerala, India Research Scholar, Dr. Hermann Gundert Central Library and Research Centre, Kannur University, Kerala, India Shahul Hameed Koombail Principal(Retired), Government Arts and Science College, Uduma, Kasaragod 671318 Journal Article 2025 01 06 A signed graph $\Sigma=(G,\sigma)$ is a graph $G$ together with a signature function $\sigma$ which assigns $1$ or $-1$ on the edges of $G$. Seidel matrix of an unsigned graph is already defined and researchers investigated some of its spectral and other properties. Considering the recently introduced notion of signed distance in signed graphs and that of the distance compatible signed graphs, we define distance induced Seidel matrices for such signed graphs and analyze their spectrum mainly for some classes of unbalanced distance compatible signed graphs, as balanced signed graphs possess the same distance induced Seidel spectrum as that of its underlying graph. We also deal with the distance compatibility issue in the line graph of a distance compatible signed graph and discuss the corresponding distance induced Seidel spectrum in this regard. https://comb-opt.azaruniv.ac.ir/article_14983_b9fb4a9c361c75db1107ba35454eb4ca.pdf